Library 


A       £  0_IJ  R  IS  E 
in  the 


Chas.  C.  Swafford,  M.  S. 

// 

Instructor   in  Civil  Engineering 
University  of  California 

Prepared  Especially  for  the 
Extension  Di%Tision 

of  the 
University  of  California 


Berkeley.,   California 
1920 


Engineering 
Library 


TY  OF   CUJPOtNlA.  INTENSION 
Course   1A-1B  Elements   of  Survey  ing  Stafford 


Contents 


Preface,  Plan  of  the  Coarse,  Introduction. 


Assignment  I.  Definitions,  Outline  of  Purpose  o;?  Surveying. 

II.  Linear  Measurements. 

III.  Nature  of  Errors  in  Measurements. 

IV.  Adjustment  of  Errors  in  Measurements. 

V.  The  Compass  and  its  Uses. 

VI.  Compass  Surveying. 

VII.  The  Level  and  its  Uses. 

VIII.  Problems  in  Leveling. 

IX.  The  Transit  and  its  Uses. 

X.  The  Transit,  Ranging  Lines  and  Measuring  Angles. 

XI.  The  Transit,  Observing  on  Polaris  for  Azimuth  c.nd 

Altitude. 

XII.  The  Transit,  Solar  Apparatus. 

XIII.  Adjustment  of  Instruments. 

XIV.  Adjustment  of  Instruments  (continued). 

XV.  Land  Surveying,  Methods  of. 

XVI.  Lanu  Surveying,  Latitudes  and  Departures,  Co-ordinates. 

XVII.  Land  Surveying,  D.  M-  D's.,  Areas. 

XVIII-  Land  Surveying,  Supplying  Omissions,  Parting  off  Land. 

793909 


Page  2 


XIX.  Surveying  of  the  public  Lands,  U.  3.  System. 

XX.  Surveying  of  the  Public  Lands,  Tangent  and  Secant 

Methods,  Convergence 
xA  \\Z  of  Meridians. 


XXI.  Stadia  Methods  of  Surveying. 

XXII.  Stadia  Methods  of  Surveying,  Stadia  Reductions. 
XXIII.  Profile  Leveling,  Contours,  Grede  Lines. 
XXIV.  Cross  Section  Leveling,  Volumes,  Excavations. 

XXV-   Cuts  and  Fills,  Sectioning  and  Contours. 
XXVI.  City  Surveying,  Rectangular  Systens. 
XXVII.  City  Surveying,  Co-ordinate  Systems. 
XXVIII.  Simple  Curves,  Streets  and  Roads. 

XXIX.  Railroad  Surveying,  Tangents  and  Curves. 

XXX.  Railroad  Surveying,  Stopping,  Location,  Grading. 
XXXI.  Base  Line,  tieasurements  and  Establishing  of. 
XXXII.  Triangulation,  Method  and  Uee. 
XXXIII.  Topographical  Surveying,  Details  end  Contours. 
XXXIV.  The  Planetable  and  its  Uses. 
XXXV.  Planetable  ,  Methods  anfi  Problems. 
XXXVI.  Mine  Surveying. 
XXXVII.  Hydrographic  Surveying. 
XXXVIII.  Mapping  and  Office  Work,  Computing. 

XXXIX.  Rights,  Duties,  and  Privileges  of  the  Surveyor. 

XL-  Rights,  Duties,  and  Judicial  Functions  of  the  Surveyor. 


Page  3 
?I,iM  OF  THE  COURSE 

This  course  in  flane  Surveying,  offered  by  -the  Extension 
Division  of  the  University  of  California  comprises  forty  (40)  assign- 
ments, each  treating  some  definite  part  of  the  subject,  and  aiming 
in  their  scope  to  present  the  work  embraced  in  the  regular  surveying 
courses,  Civil  Engineering  1A,  IB,  and  C.  E.  3,  College  of  Civil 
Engineering,  University  of  California;  excepting,,  that  in  the  Ex- 
tension course  the  problems  for  i'ield  tolution  and  practice  with 
instruments  have  bean  specially  selected  and  arranged  for  your  work 
without  the  immediate  supervision  of  an  instructor. 

The  problem  work,  therefore,  calls  for  special  care  on  your 
part.  You  should  givo  pM-ticular  heed  to  (1st)  the  purpose;  (2nd) 
the  method;  (3rd)  the  care,  refinements,  and  precision  of  the  work; 
(4th)  the  record  of  field  notes  -  sketches,  illustrations,  diagrams, 
etc.  ,  and  (5th.)  the  result  -  the  lesson  learned  or  the  training 
gained. 

i'he  plan  of  this  eourse  requires  that  you  shall  study  each 
assignment  in  acarei'ul,  painstaking  way;  not  merely  reading  it  over, 
nor  even  committing  it  to  memory,  out  maicing  a  full  and  critical 
study  of  each  part,  so  as  to  gain  a  clear  understanding  of  the 
thought  content,  to  see  its  bearing  on  the  subject  of  surveying  as 
a  whole,  and  thus  to  acquire  step  by  step  the  science  of  surveying. 

References  are  given  in  each  assignment  to  standard  texts 
on  the  subject  of  surveying,  including  Tracy,  Johnson,  Breed  & 
Hosmer,  and  Raymond.   Of  course  it  is  not  likely  that  you  -.Till  have 


Plan  of  the  Course  Page  4 

access  to  all  or  even  several  of  these  works,  but  it  is  hoped  that 
you  may  have  one  or  more  of  them,  and  also  a  manual  of  surveying 
instruments,  such  as  published  by  manufacturers  descriptive  of 
their  good?.   These  manuals  contain  much  information,  tables,  hints, 
etc. ,  of  value  to  the  engineer.  Attention  is  called  here  to  those 
issued  to  the  engineering  profession  by  Bausch  rjid  Lorab,  Rochester, 
New  York,  C.  L.  Berger  and  Sons,  Boston,  Mass.,  W.  and  L.  E.  Gurley, 
Troy,  New  York,  and  others,  which  may  be  procured  at  small  cost  by 
addressing  the  firms  named  above.  The  General  Land  Office,  Washing- 
ton, D-  C.,  aleo  has  in  preparation,  a  Manual  on  the  Survey  of  the 
Public  Lands,  which  may  be  had  for  a  small  fee  from  the  Bureau  of 
Publication,  Washington,  D.  C.  Preferences  will  frequently  be  made 
to  the  foregoing  works,  and  their  careful  perusal  is  earnestly  urged. 

Accompanying  each  assignment  are  questions  to  be  answered, 
problems  to  be  solved,  and  field  exercises  to  be  worked  out.  Your 
papers  are  to  be  sent  to  the  Extension  Division  for  correction, 
ctiticism,  and  grading.  Your  standing  in  the  course  is  determined 
by  the  paper  you  submit;  your  progress  will  depend  largely  upon 
your  ability  to  profit  by  corrections  and  criticisms. 

Each  paper  submitted  by  you  should  be  worked  out  carefully 
and  punctiliously,  special  care  being  taken  to  place  everything, 
from  heading  to  close,  in  a  neat,  orderly  arrangement,  with  any 
field  notes,  tabulations,  or  sketches  to  accompany  the  same.  Field 

notes  and  sketches  (or  illustrations)  should  preferably  be  dene  in 

(not  write) 
pencil.   Use  a  4H  pencil  and  letter/,the  notes  in  approved  styles. 


Plan  of  tiie   csou^pe  Page  5 

(See   illustrative,    specimen  pages   of  Field  Jotes  displayed   in  the 
assignments  fro-i  time  to  time.) 

The  required  computatioas  :auet  lie  _pade   in.  good  arrangement, 
all  operations  clearly  stated,   and  conclusions  or  answers  properly 
indicated.      The  actual  work   of  multiplication,    division,    extraction 
of  roots,   etc.,   need  not  be   returned  with  the    solutions,   but  the 
processes   and  their  results  niust  De  clearly  shown.      Logarithmic 
computations   should  gi've  the  logarithms  used.     Where  slide  rules 
or  other  natherr-atical  devices  are  employed,   the  fact   thould  be 
definitely  stated.     Where  tables  are  used,  the  title  and  source 
should   likewise   oe  mentioned.      This   of  course   does  not  apply  to 
tables   of   logarithms,   powers  and  roots,  etc. 

In  all  your  trork  bear   in  mind  that  the  purpose  is  to  acquire 
a  knowledge,  not  only  of  the  subject  of  surveying  as  a  theory,   but 
of  its  methods  and  expressions  as  embodied   in  principles,   problems, 
notes,  maps,   and  instruments  employed  in  fisld  and  office.     Without 
such  knowledge  ai\d  the  training  that  goes  with  it,   hand  in  hand, 
this  course  v/ill  be   of  small  avail   in  giving  you  the   real  training 
intended. 


Page  6 
INTRODUCTION 

Surveying,  like  most  other  work  in  applied  science,  is  an 
art.  Ihe  strict  application  of  formulas  is  not  alvays  possible.  In 
many  problems  special  devices  must  be  used,  the  correct  solution  of 
a  problem  must  be  set  aside  and  approximations,  more  or  less  crude, 
must  be  substituted  to  meet  the  rights  of  legal  ownership  under  the 
laws  of  the  land.  Errors  in  previous  surveys  of  the  same  lines  or 
areas  must  be  considered  and  corrected  or  the  new  survey  must  con- 
form to  the  actual  conditions  met  with  on  the  ground  in  spite  of 
•written  evidence  to  the  contrary. 

To  accomplish  such  things,  then,  the  surveyor  must  be  a  man 
at  once  honest,  sincere,  dependable,  energetic,  ingenious,  and  ob- 
servant. He  must  be  patient  in  his  work  and  with  other  people.  Ke 
must  be  ready  to  give  an  unbiased  opinion  as  to  the  rights  of  dispu- 
tants when  called  upon  to  do  so,  and  should  always  be  sure  of  the 
correctness  of  his  -.Tork  or  its  limitations  before  submitting  results 
to  his  employer  or  to  other  persons.  Ee  cust  have  a  thorough  know- 
ledge of  the  fundamental  principles  of  surveying  such  as  will  enable 
him  to  solve  all  of  his  problems  correctly. 

In  these  assignments  it  is  assumed  that  you  have  a  good  under- 
standing of  the  common  processes  of  arithmetic,  algebra,  plane  geom- 
etry, plane  trigonometry,  and  the  use  of  mechanical  dravring  instru- 
ments.  It  should  be  your  endeavor  to  acquire  a  knowledge  of  solid 
geometry,  spherical  trigonometry,  and  physics,  as  of  real  value  to 
you  in  your  studies  and  in  later  work  in  the  field. 


Introduction  Ps-ge  7 

It  is  further  a,isuued  that  you  will  ha\e  ajcese  to  the  common 
equipment  of  the  surveyor  eo  that  the  exolam-tic-ns  of  the  various 
instruments  and  the  n.ethods  of  their  p.cijustmtnt  and  use  can  be 
understood.   Lacking  such  equipment,  it  will  be  hard  for  you  to 
grasp  the  significance  of  iruch  of  the  course  and  your  studies  will 
result  in  a  training  in  geometry  and  not^  in  a  training  in  surveying 
methods. 

You  are  cautioned  not  to  juaip  to  the  common  and  errcnetras 
conclusion  that  v/hat  is  said  in  this  series  of  assignments  is  all 
that  can  be  said  on  the  subject  of  surveying.   It  is  not  iatended 
to  give  you  s^ill  as  a  surveyor,  but  to  ^ive  a  good,  general  train- 
ing in  the  fundamental  principle^  underlying  the  methods  of  the 
surveyor  in  the  field  and  office,  coupled  with  a  brief  discussion 
of  the  common  problems  met  in  practice.   Skill,  in  any  line  of 
endeavor ,  coiaeg  only  through  long  practice. 

The  real  student  will  find  suggestions  that  will  lead  him 
far  into  the  fiolci  of  surveying. 


/ssr'gnnent    1  Page  8. 

DEFINITIONS 

FOREWORD: 

In  this  assignment  it  is  intended  to  give  a  general  outline 

of  the  purpose  of  surveying  and  some  of  the  common  conceptions,  as- 
sumptions, and  definitions  necessary  to  a  proper  understanding  of 
the  more  detailed  problems  which  are  to  follow. 

(1)  SURVEYING 

The  process  of  measuring  lengths  of  lines,  magnitudes  of 

angles,  and  differences  of  elevation  at  or  near  the  surface  of  the 
earth  for  the  purpose  of  establishing  Boundaries,  establishing 
elevations  of  points,  map-making,  and  construction,  is  called 
surveying. 

(2)  TEE  EARTH 

The  earth  is  approximately  a  sphere.      The  diameter  from 

pole  to  pole   oeing  26.37  miles  shorter  than  a  diameter   in  the  plane 
of  the  equator,  the  equatorial  diameter,  as  computed  oy  Clarke  in 
1866  and  adopted  by  the  U.    L.    Coaet  and  Geodetic  Survey,    is 
41,852,124  feet,  rrhile  the  corresponding  polar  diameter   is  41,710,242 
feet. 

(3)  a; A- LEVEL 

The  fundamental  datum  for  elevation  of  points  on  or  near 
the  surface  of  the  earth  is  taken  at  sea  level.   The  layer  of  water 
covering  the  greater  portion  of-  the  earth  has  nearly  the  same  form 
as  the  mean  globe.  A  slight  variation  is  due  to  the  action  of  the 
tides  and  the  rotation  of  the  earth  on  its  axis.   Since  there  is  a 
rise  end  fall  of  tide  twice  a  day  for  any  one  locality,  it  has  been 


Klem.    of  Sur-  Li.  As  -signment    1  Page  &• 

decided  that  the   MEM   UVF.L  of  the  ocean  ivill  be  called  sea-level. 
In  all  the  common  determinations  of  elevations  sea- level  is  said 
to  have  a  zero  elevation. 

A  point  well  worth  remembering  is  that  most  of  the  problems 
in  surveying  occur    above   sea-level. 

(4)  MERIDIANS 

Imaginary  lines  passing  completely  around  the  earth  and 

forming  a  closed  carte  two  points  of  which  lie  in  the  north  and 
south  poles  of  the  globe  are  called  meridians.   To  illustrate — 
Imagine  that  a  person  starts  from  a  point  on  the  surface 
of  the  earth  and  travels  due  north  until  the  north  pole  is  reached. 
Continuing  through  the  pole  in  the  same  line,  not  deviating  from 
it  in  any  way,  his  course  will  be  due  south  until  he  reaches  the 
south  pole;  thence  he  travels  due  north  to  his  original  position. 
The  path  traversed  IE  a  meridian. 

The  geometric  and  astronomical  definition  is  as  follows: 
A  meridian  is  the  line  on  the  surface  of  the  earth  cut  by 
a  plane  passing  through  the  north  and  south  poles  of  the  earth. 

(5)  PARALLELS  OF  L^IIUDE 

Parallels  of  latitude  are  imaginary  circles  on  the  surface 

of  the  earth  lying  in  planes  parallel  to  the  plane  of  the  equator 
and  having  their  centers  in  the  line  joining  the  poles  (polar  axis) 
of  the  earth. 

(6)  LONGITUDE 

The  angular  distance  from  an  agreed  fundamental  meridian  to 


Elea.  of  Curv.  IA        Assignment  1  Page  10 

the  Eeridian  through  the  point  in  question,  measured  in  the  plane 
of  the  parallel  of  latitude  through  the  same  point,  is  the  longi- 
tude.  The  fundamental  (prime)  meridian  for  English-speaking 
countries  is  through  Greenwich,  England.   Longitudes  are  measured 
East  and  West  from  Greenwich,  in  each  direction  from  0°  to  180°. 

It  is  to  te  noted  that  Icngf.tu^e  is  the  angular  Treasure  EO 
that  while  meridians  converge  toward  the  pole  and  the  linear  dis- 
tance between  them  gets  less  as  the  pole  is  approached,  the  longiv 
tude  of  tne  meridian  in  question  does  not  change  so  long  as  neither 
pole  is  passed. 

(7)  LATITUDE 

Latitude  is  the  angular  distance  from  the  Equator  north  or 
south  to  the  parallel  of  lax  itude  through  the  point  in  question, 
measured  in  the  plane  of  the  meridian  through  the  point.    Latitudes 
range  fron  0  degrees   at  the  Equator   to  90  degrees  at  the  poles. 

(8)  A  PLUMb   LINE 

The  line  determined  by  the  position  of  a  cord  at  the  lower 

end  of  T'hich  is  fastened  s.  weip,ht  sufficient  to  stretch  the  cord 
into  a  straight  line,  the  cord  then  being  suspended  in  quiet  air 
and  allowed  tc  come  to  rest,  is  called  a  plumo  line. 

A  common  definition  of  a  pluino  line  is  about  as  follows: 

h.  plunb  line  is  a  line  pointing  toward  the  center  of 
the  earth,  i.  e.,  a  radius  of  the  earth  prolonged.   This,  however, 
ie  not  strictly  true  owing  to  the  rotation  of  the  earth  and  the 
irregular  distribution  of  mass  within  the  earth.   In  the  northern 
hemisphere,  generally,  the  plumb  lines  point  slightly  south  of  the 


Elem.  of  Surv.  Ih.         Assignment  1  •Page  11 

geometric  center  or  the  earth. 

Ko  two  plumb  lines  are  parallel. 

A  plumb  line  points  to  what  is  known  as  the  ZENITH  or  the 
point  in  the  heavens  vertically  overhead  at  any  point  on  the  earth's 
surface,   -t-'he  NADIR  is  a  corresponding  point  found  by  prolonging 
the  plumb  line  through  the  earth  to  a  diametrically  opposite  point 
on  the  celestial  sphere. 

(9)  A  LEVEL  SURFACE 

A  surface  that  is  everywhere  perpendicular  to  the  plumb 

line  is  a  level  surface.   Thus,  it  is  seen  that  a  level  surface1  is 
not  a  flat  surface  or  a  plane,  but  a  curved  surface  conforming, 
approximately,  to  the  general  shape  of  the  earth. 

(10)  A  LEVEL  LIRE 

A  level  line,  is  then,  a  line  in  this  curved  surface  and  is, 

itself,  curved.  What  is  ordinarily  called  a  level  line  is  a  geo- 
metrically straight  line  tangent  to  a  level  line  at  which  point  of 
tangency  the  straight  line  is  perpendicular  to  the  plumb  line.  A 
level  line,  on  the  other  hand,  is  perpendicular  to  any  plumb  line 
that  may  intersect  it. 

(11)  A  STRaiGET  LINE 

j- 

A  straight  line  on  the  surface  of  the  earth  is  really  a 
portion  of  a  great  circle  of  the  earth,  e.  g. ,  a  meridian  is  a 
straight  line.   A  geometrically  straight  line  is  one  that  would 
be  tangent  to  a  sphere  if  drawn  perpendicular  to  a  plumb  line,  or 
would  pass  through  the  surface  of  the  sphere  in  two  points  or 
would  net  touch  the  sphere  at  all  -  all  three  cases  are  possible. 


Elem.  of  Surv.  IA        Assignment  1  Page  12 

A  geometrically  straight  line  would  possibly  cut  through  the  sur- 
face of  the  earth  in  more  than  two  places  owing  to  inequalities 
of  the  surface. 

(12)  GEODETIC   SURVEYING 

The  branch  of  surveying  which,  owing  to  the  extent  of  the 

surveys,  t^K&E  into  consideration  the  spheroidal  fora  of  the  earth 
is  termed  Geodetic  Surveying.   That  is,  in  the  survey  of  a  conti- 
nent or  state  the  lines  are  so  long  that  they  are  appreciably 
curved  and  the  aigles  of  the  various  polygons  making  up  the  sur- 
vey are  angles  of  spherical  polygons.   This  type  of  surveying  is 
very  difficult,  requiring  men  of  special  training  and  experience 
in  the  prosecution  of  both  field  and  office  worK. 

(13)  PLANE  SURVEYING 

The  branch  of  survey ing" which,  owing  to  the  limited  extent 

of  the  surveys,  does  not  consider  the  spheroidal  fora  of  the  earth, 
is  known  as  plane  surveying.   In  other  words  the  assumptions  made  are. 

1.  A  level  surface  is  a  flat  surface. 

2.  A  level  line  is  a  straight  line. 

3.  A  "straight  line "  on  the  earth  is  geometrically  straight. 

4.  All  plumb  lines  within  the  limits  of  the  survey  are 
parallel. 

5.  All  angles  of  a  polygon  are  plane  angles. 

This  branch,  the  more  common  and  elementary  of  the  two  types, 
will  constitute  the  greater  part  of  the  work  of  this  course. 

(14)  NATURE  CF  MEASUREMENTS  IK  PLh.NE  SURVEYING 

Surveying,  as  before  stated,  is  for  the  purpose  of  determining 


Elem.  of  Surv.  1A        Assignment  1  -Page  13 

the  relative  positions  of  points  and  lines  on  or  near  the  surface 
of  the  earth.  A  moment's  reflection  will  bring  you  to  the  reali- 
zation that  in  the  use  of  the  common  equipment  of  the  surveyor  the 
only  things  possible  to  determine  are  the  positions  of  points,  the 
distances  (both  horizontal  and  vertical)  between  them.  sand,  the  an- 
gles between  lines  and  planes.   In  determining  the  shape  of  a 
field,  a  building,  or  a  cross-section  in  question  the  surveyor 
merely  takes  a  sufficient  number  of  measurements  to  enable  him  to 
establish,  geometrically,  the  outline  of  the  thing  measured. 

Where  possible,  it  .  may  be  best  to  take  direct  measure- 
ments of  the  line  or  angle  under  consideration.  Uut  direct  measure- 
ments may  involve  physical  difficulty  and  lack  of  what  is  called 

"reasonable  accuracy".  For  example,  it  may  be  possible  to  tape 
the  length  of  a  line  across  a  swarip  or  a  line  across  hill  and  valley 
for  a  long  distance,  but  the  error  in  the  work  and  the  physical 
exertion  will  often  be  far  in  excess  of  vrhat  is  reasonable.   It  is 
usually  possible  to  find  some  device  by  which  such  a  determination 
may  be  made  indirectly  so  that  the  result  will  be  more  accurate  aid 
the  work  of  measurement  far  less  troublesome  and  exhausting. 

(15)  ACCURACY  VERSUS  COST 

Nearly  all  work  in  surveying  can  be  cone  very  accurately, 

but  it  is  neither  necessary  or  advisable  to  attempt  to  maintain  a 
high  degree  of  accuracy  in  all  problems,  nor  to  make  all  measure- 
ments in  different  parts  of  the  same  problems  equally  accurate.   If 
&  survey  is  being  made  tc  find  the  acreage  of  a  field  planted  to  a 
certain  crop  and  the  area  is  to  be  determined  to  the  nearest  one-tenth 


Elem.  of  Surv.  LA.         Assignment  1  jPage  15 

the  nearest  ten  or  fifteen  minutes  and  the  lengths  of  the  courses 
to  the  nearest  link  (7.92  inches).  A  later  survey  is  made  of  the 
property,  but  the  value  of  the  land  has  increased  to  $200  per  acre, 
in  which  case  the  surveyor  should  measure  the  boundaries  of  this 
field  with  the  transit  end  steel  tape  determining  the  angles  to  the 
nearest  minute  and  the  distances  to  the  nearest  one-tenth  of  a  foot. 
It  is  not  to  be  understood  that  this  accuracy  is  in  strict  ratio 
to  the  increase  in  value  of  the  property  nor  should  it  be  assumed 
that  the  new  measurements  will  check  the  old  but  roughly.   If  the 
original  surveyor  executed  his  work  properly  and,  though  his  meas- 
urements were  more  or  less  in  error,  set  proper  monuments  which 
can  be  found  intact  by  the  later  surveyor,  the  new  survey  will  be 
a  survey  of  the  same  field.   Unfortunately,  however,  the  earlier 
surveyors  did  not  consider  the  possibility  of  a  -.later  survey  or 
were  apt  to  be  careless  about  such  things;  consequently  much  labor 
and  expense  is  the  lot  of  the  surveyor  who  raakes  the  more  accurate 

survey.   It  is  seen  that  a  large  question  of  rights  and  what  con- 

liae 

stitutes  the  true  position  of  a  boundary>is  opened  up  by  such 

problems. 

(16)  KINDS  OF  MEASuREioENTS  MADE   B.  PLaNfc  SURVEYING 

TiShen  the  area  of  a  field  is  given  as   160  acres  the  area 

meant   is  that  of  the  polygon  formed  by  projecting  the  boundaries 
of  the  field  onto  a  horizontal  plane.      It  may    be  that  the   boundaries 
of  the  field  are  on  a  hillside  and   do  not   lie    in  horizontal   planes, 
but   experience  has   shown  that  it  would  be  difficult   and   impracticable 
to  consider  the    lengths   of  the   lines  that  would  be  found  by  following 


Elera.  of  Surv.  1A         A&.JJ  gvime.it  1  -i'ags  16 

the  slope  of  the  ground.   It  is  seen,  then,  that  what  is  called 
the  length  of  a  line  in  surveying  is  the  horizontal  projection  of 
the  line  (Hhis  rule  holds  unless  the  length  is  qualified  by  sone 
term  such  as  "slope  length",  etc.).   Usually  the  measurement  of  a 
line  is  made  so  that  the  horizontal  projection  is  obtained  directly. 

In  a  similar  manner  the  angles  of  a  polygon  on  the  ground 
are  given  as  the  angles  between  the  horizontal  projections  of  the 

lines. 

In  problems  where  the  difference  in  elevation  of  points  is 
important  the  measurements  of  such  quantities  are  usually  made  so 
as  to  give,  directly,  the  vertical  distance. 

There  are  numerous  cases  arising  -mere  the  distance  between 
two  points  will  be  measured  on  a  slope.   In  such  cases  the  vertical 
angle  must  be  determined  or  the  vertical  difference  in  elevation 
between  the  extremities  of  the  line  must  be  found  IB  sake  it  pos- 
sible to  compute  the  horizontal  distance.   *lhere  the  slope  distance 
and  the  vertical  angle,  or  where  the  slope  distance  and  horizontal 
distance  are  given,  it  will  be  possible  to  find  the  difference  in 
elevation.   INhen  such  a  slope  measurement  is  taken,  it  is  subse- 
quently reduced  to  a  horizontal  distance  and  to  a  vertical  difference 
in  elevation. 

fo  summarize: 

1.  Distances  are  usually  horizontal. 

2.  Differences  in  elevation  are  usually  vertical. 

3.  Angles  are  measured  in  a  horizontal  plane  or  a  vertical 

plt-ne. 


Elem.    of  Surv.  IA  A3Rigr.ir?nt   1  Page   17 

4.    If  measurements  of  any  linear  or  angular  quantities  are 
are  made  in  other  ways,   they  are  usually  reduced  to 
vertical  and  horizontal  quantities. 


HIOBIEMS 

1.  Show  by  a  diagram,  carefully  constructed,  that  no  two  plumb-lines 

are  parallel. 

2.  Show  that  a  level  line  between  two  points  on  the  earth  s  surface 

is  longer  than  a  straight  line  joining  the  same  points. 

3.  Prom  the  values  of  equatorial  and  polar  diameters  given  on  page  8, 

Assignment  1,  compute  the  length  of  one  minute  of  arc  of 
longitude,  and  the  mean  length  of  one  minute  of  arc  of  latitude. 

4.  Determine  v;hich  is  greater,  the  superficial  areaof  a  sloping  field 

or  the  acre&.ge  as  measured  by  the  usual  methods  of  plane  survey- 
ing. Give  reasons  for  following  the  methods  of  surveying  land 
areas. 


You  will  confer  a  favor  upon  the  instructor  and  upon  other 
students  if  you  point  out  anything  in  the  assignments  of  this 
course  which  seems  to  be  obscure.  Write  questions  to  the  instructor, 
if  you  care  to  do  so,  when  you  send  in  your  papers. 


TOHTEfiSIiT  OF  CALIFORNIA  EXTENSION  D IV  IE  10?! 
CORKESi'CNDLNCE-STUDr  CCUK23S    IN   TECHiiZICAL  SUBJECTS 

Course   IA.  Elements  of  Surveying  Stafford 

Assignment   2 
LINEAR  MRjiSUREMFPTS 

FOREWORD : 

1'he  following  discussion  treats  of  the  measurements  of 

linear  distances,  particularly  of  those  along  the  surface  of  the 
earth,  or  what  are  generally  designated  as  horizontal  measurements. 
V?-rious  types  of  measuring  devices  will  be  illustrated  and  des- 
cribed snd  particular  emphasis  laid  upon  the  more  common  methods 

of  measurement. 

-oOo- 

(17)  A  LIK&.aF.  DISI&NCE 

the  distance  or  length  in  a  straight  line  between  two  points, 

is  called  the  linear  distance  between  those  points.   The  linear 
measure  or  magnitude  of  the  distance  is  expressed  in  terms  of  some 
established  or  arbitrary  unit,  e.  g. ,  a  linear  distance  of  9  feet 
may  be  expressed  as  9  feet,  3  yards,  108  inches,  or  3  2/5  paces, 
the  unit  used  depending,  largely,  upon  the  ncture  of  the  problem 
and  the  custom  of  the  person  making  the  measurement. 

(18)  THE  UNITS  OF  LiEASUHE 

The  units  used  in  the  united  States  by  the  surveyor  are 

either  of  English  or  French  origin,   the  English  units  have  the 

following  relations: 

Linear  Measure  Square  Measure 

12  inches  =  1  foot  144  sq.  inches  =  1  sq.  foot 

3  feet   -  1  yard  S  sq.  feet  =  1  sq.  yard 

5  1/2  yards  =  1  rod  30  1/4  6}.  yards  -  1  sq.  rod 

16  1/2  feet   =  I  rod  160  sq.  rods  =  i  &cre 

32C  rods   =  1  mile  43,560  sq,  feet  =  1  acre 

5280  feet   -  1  mile  640  acres  =  1  sq.  mile 

Volumes 

1728  cu.  inches  -   1  cu.    foot 

27   cu.  feet        =  1  cu.    yard. 


Elem.  of  auv.  IA         /.ssignn-sn*  2  P-ge  2 

An  important  system  of  units,  of  Bnglish  origin,  used  by  the 
surveyor  is  based  on  the  rod.  A  measuring  device  knovn  as  the  Gun- 
tec's  Chain  is  made  just  4  rods  or  66  feet  long.   This  length  is 
divided  into  100  parts,  called  links,  each  link  having  a  length  of 
7.92  inches,  hence  a  table  of  measures  ma^  be  written  in  terms  of 

links  and  chains  : 

Linear  Measure  Square  Measure 

10  links  =  1  rod  100  sq.  links  =  1  sq.  rod 

100  links  =  1  chain        10000  sq.  links  =  1  eq.  chain 

1  chain  =  66  feet  1  sq.  chain  =  16  sq.  rods. 

80  chains  =  1  mile  10  sq.  chains  =  1  acre 

6400  sq.  chains  =  1  eq.  mile 

French  units  of  measure  are  cased  on  the  International  Metre 

and  are  as  follows: 

Linear  Measure 

10  millimetres  -  1  centimetre 

10  centimetres  =  1  decimetre 

10  decimetres  =  1  metre  =  39.37  inches  (English) 

10  metres      =  1  dekametre 

10  dekametres  =  1  hektometre 

10  hektometres  =  1  kilometre  =  1000  metres 

Square  Measure  Volumes 

100  sq.  mm.  •=•  1  sq.  cm.  1000  cu.  mm.  =  1  cu.  cm. 

100  sq.  cm.  =  1  sq.  dm.          1000  cu.  cm.  =  1  cu.  dm. 

100  sq.  dm.  =  1  so.  m.  10GO  cu.  dm.  =  1  cu..  m. 

100  sq.  m.   =1  are 

100  ares    =  1  hectare 

IOC  hectares  -  1  sq.  kilometre 

In  times  past  and  in  the  present  day  the  English  system  of 
units  has  been  the  more  common  in  this  country.  The  Gunter's 
chain  was  usad  in  much  of  the  land  surveying  done  in  the  early 
history  of  nearly  everv,  part  of  the  United  States.   The  reason  is 
obvious  when  one  under stands  the  eimple  relation  of  the  chain  to 
the  mile,  acre,  and  section.   Consequently  many  deeds  and  records 


Llem.    of  3urv,  iA  As  *?  ig^merrt  2  Page  3 

of  early   surveys  appear   in  chains.      For  this   reason  the   surveyor 
should  become  thoroughly  familiar  with  this  system  of  units. 

Later   surveys,   v:here    land  has  become  valuable,   usually  give 

X 

the  linear  dimensions  in  feet  and  fractions  thereof.   In  this  con- 
nection it  should  be  pointed  out  that  the  surveyor  usually  takes 
measurements  of  linear  quantities  in  feet  and  decimal  fractions 
of  feet.   In  other  words,  a  foot  is  divided  into  tenths,  hundredths, 
etc.,  and  a  distance  is  given  as  756.78  feet  rather  than  as  feet, 
inches,  and  fractions  of  inches.  Again,  the  surveyor  should  be 
familiar  v/ith  the  relation  of  decimal  fractions  of  a  foot  to  inches 
so  that  he  can  quickly  change  measurements  to  ordinary  units  for 
mechanics  and  others  net  farailiar  with  such  fractions. 

TAbLS  I 
Decimals  of  a  Foot  in  Inches. 


Decinal  of  a  foot 

Inches 

0.01 
0.0* 

•: 

1/8- 
1/2- 

0.08 

— 

1- 

0.17 

^ 

Z+ 

0.25 

= 

3  exact 

C.  37. 

— 

4- 

0.50 

- 

6  axact 

G.7o 

— 

9  exact 

for  rough  approximations  the  above  equivalents  will  be  found 
convenient,  though  for  precise  work  it  Trill  be  necessary  to  carry 
the  relation  out  to  a.  riner  uegree  of  accuracy. 

The  French  (or  Metric)  system  is  shown  for  the  reason  that 
many  surveyors  are  constantly  leaving  this  country  for  countries 
•where  such  units  are  employed  and  because  much  of  the  work  of  the 


Elero.  of  Surv.  1&         Assignment  2  ^age  4. 

U.  S,  Coast  e.nd  Geodetic  purvey  and  other  depaitaents  of  tne  United 
States  Government  is  carried  out  in  metric  units. 

(19)  MEASURING  DEVICES 

The  commonest  measuring  device  is  the  ordinary  foot  or  two- 
foot  rule.  A  finely  constructed  rule  or  scale  of  one  foot  in  length 
is  used  by  the  engineer  or  surveyor.   The  graduations  are  given, 
usually,  in  deciirai  fractions  of  inches.   This  rule  is  used  chiefly 
for  office  work  in  making,  scale  drawings,  out  it  will  often  have  a 
proper  plr.ce  in  precise  measurements  in  the  field.  The  common 
type  of  folding  carpenter's  rale  is  well  known  to  almost  everyone 
interested  in  the  mechanical  arts.   This  rale  is  graduated  variously 
most  commonly  in  inches  and  sixteenths  of  an  inch. 

The  yard  stick  and  ten-foot  pole  are  used  in  short,  rough 
measurements.   Formerly  the  ten-foot  pole  r/as  used  in  certain 
types  of  surveying  problems. 

The  cloth  tap a ,  jade  of  a  linen  strip  and  graduated  to 
feet  and  inches,  while  used  in  some  rough  work,  has  very  little 
place  in  most  surveying  vork,  as  it  soon  streiches  or  shrinks  so 
as  to  make  it  too  inaccurate  for  reliability. 

The  metallic  tape  is  made  by  weaving  fine  bronze  wires 
lengthwise  through  a  heaiy  linen  strip.   This  strip,  usually  fifty 
feet  long,  is  painted  a  light  color  and  the  foot  marks  a^id  frac- 
tional division  are  printed  on  it.   The  bronze  wires  are  supposed 
to  prevent  undue  shrinkage  and  stretching,  but  they  serve  their 
purpose  indifferently.   Such  tapes,  however,  are  found  very  useful 


Elem.  of  Surv.  -".A        Assignrient  2  -^age  S 


in  taking,  short  measurements  on  offsets,  and  for  road  cross-sectioning. 
These  tapes  may  be  obtained  aither  mounted  or  unmounted,   'fhe  reel 
is  usually  enclosed  in  a  heavy  leather  box.   If  the  tape  is  to  be 
ueed  where  mud  and  water  are  encountered  it  should  be  taken  off 
the  reel  as  the  box  will  soon  beco.ned  choked  up  with  debris  of 
various  kinds  carried  in  by  the  tape.   The  tape  should  be  carefully 
dried  before  it  is  replaced  on  the  reel. 

The  steel  tape  is  the  most  useful  of  all  the  measuring  de- 
vices to  the  f.  urveyor  .   There  are  many  varieties  of  steel  tapes 
ranging  from  very  light  "ribbon"  tapes  to  hetorr  tapes  of  the  rib- 
bon or  "-wire"  type.  The  light  tapes  are  thin  strips  of  spring 
steel  graduated  to  feet  and  inches  or  to  feet  and  decimals  (the 
common  types  to  hundredths  of  a  foot).   Such  tapes  are  never  over 
100  feet  long  and  seldom  over  50  feet. 

Heavy  steel  tapes  such  are  are  used  in  most  surveying  are 
heavy  strips  of  spring  steel  graduated  to  feet  with  the  first  and 
last  foot  divisions  on  the  tape  graduated,  usually,  to  tenths  of 
a  foot,  though  they  may  be  purchr.sed  with  the  end  feet  graduated 
to  hundredths  of  a  foot.   I'he  graduations  are  marked  in  different 
ways  ranging  from  0  feet  to  100  feet. 

In  the  heaviest  patterns  the  tapes  are  graduated  every  five 
or  ten  feet  with  the  l?.st  five  or  ten  feet  graduated  to  feet  and 
the  last  foot  subdivided  to  tenths  of  a  foot.   These  tapes  are 
often  from  500  to  10CO  feet  long. 

The  light  tapes  are  usually  obtained  on  metal  reels  while 


Elem.  of  Surv.  -1-/.         Aseignrent  2  Page  6. 

the  heavier  patterns  are  usually  ura^ouirtea.   It  is  possible  to 
purchase  reele  for  the  heavy  tapes.   Such  a  real  should  be  of 
rather  large  diameter  and  of  the  "open"  pattern. 

The  Gunter's  chain  ^ though  fast  becoming  obsolete)  is  a 
sturdy  measuring  device  66  feet  in  length.   It  is  made  up  of  a 
series  of  links  with  metal  handles  at  both  ends.  £.  link,  sd-called, 
ic -compose '•  of  a  long,  bar  with  a  sraall  oval  link  at  each  end.   The 
length  of  the  three  parts  of  ths  link  tsucen  together  is  7-92 
inches,  or  1/100  cf  the  length  of  the  chain.  The  end  links  are 
still  more  complex,  the  bar  link  being  divided  into  two  parts. 
On  the  outer  end  of  the  last  portion  of  this  link  is  fastened  the 
handle.   The  handle  is  to  fastened  to  the  link  that  it  forms  a  part 
of  the  length  of  the  link,  and  ie  adjustable  by  means  of  a  nut  and 
screw,  raa'cing  it  possible  to  correct  the  total  length  of  the  chain. 
Everv  tenth  link  is  marked  vrith  &  metal  tag  -  at  the  tenth  link  i& 
a  tag  with  one  point,  at  the  twentieth  link  a  tag  -vith  two  points, 
etc.   The  fiftieth  link  is  marked  oj  a  tat;  of  some  peculiar  design, 
usually  round,   oince  the  chain  is  marked  in  a  similar  manner  from 
both  ends,  care  must  be  taken  to  determine  TJhether  or  not  the 
measurement  ie  less  or  more  than  fifty  links  for  fractions  of 
chain-lengths. 

The  engineer's  chain  is  similar  i-i  type  to  the  Gunter  s 
chain,  the  only  important  dil'ference  being  that  this  chain  is  100 
feet  long  and  the  links  are  1  foot  in  length.   Both  of  these 
chains  have  been  replaced  by  the  more  convenient  and  reliable 


.    ol   Surv.    L*.  >,ssignr;ent   Z  jps.ge  7 

Among  the  man;-   useful  raeasa:  ing  devices  usea  by  the   engi- 
neer or  surveyor   is  the    stadia.      This   is  t   eoaiu-ination  of  cross- 
-.vires  in  the  telescope   of  tae  transit  or  plane  table  alidade  such 
that  tne  intercept  on  '\  rod,   as   determined  Jay  these  srosswires, 
multiplied  by  e   certain  constant  will  be  the  horizontal  distance 
from  the  instrument  to  the  point  Tnfhere  the  rod  is  held^      It   is  not 
a  perfect  method,    out  under   some  conditions   it  will  be  found  to  be 
'vaitfc-  ace  irate  as  compared  to  measurement  ".>'itn  tne  tspe. 

For  approximate  determination  of  distances,   pacing,    in  con- 
junction with  the  pedoaeter   is  found  to  be  very  useful.      The  pedom- 
eter is  a  watchlike   instrument  which  records,    in  one  type,   the  num- 
ber  of  paces  taken  bj  the  person  carrying  it.      In  another  type  the 
record  is   the  distance  in  feet,  yards,  aietres   or  liiles  -  in  this 
pattern  it   is  possible  to  regulate   the  inttruaient  to  the   average 
length  of  the  carrier's  pace. 

(20)  ICASU3IKG  OF  LIHLS 

The  me-  eiv-ement   of   ! !:••>.€ s  with  the  rul«r   flnd  i^ith    similar 

devices   has  but   little   ^lace   in  the   ordinary  routine   of  the   sur- 
veyor  £  "work.      On   the    other   hand,   the  measurement  of  distances   by 
pacing,  or  v.'itL  the  ta^c   <i.c  ^hain  or   by  .jeaiia  ol  the  stadia  forius 
a   large  part   of  the  rrany   problems  he  meets.      Of  the   last  method 
more  will   be   sairt  in  a    later  portion  of  the  course. 

(21)  RLCEG 

Pacing  is  much  more  useful  than  commonly  i/iagined,   a  re- 

jnarxable  degree  of  accuracy    oeing  obtainable.      Pacing  serves  a 

very  useful  purpose  as  a  neans   of  checking  -nore  accurate  measurements 


Elem.  or  Surv.  1^.         Assignment  2 

so  that  grose  errors  will  not  creep  into  lon^  distances,  e.  g. , 
such  as  dropping  a  tape- length,  etc. 

To  pace  a  distance  properly  it  is  first  necessary  to  deter- 
mine the  length  of  pace  or  the  number  of  paces  in  an  integral  num- 
ber of  feet.   Some  surveyors  prefer  to  develop  an  artifical  pace 
of  tnree  feet,  but  in  general  it  is  probably  better  to  maintain  a 
customaty  length  of  pace  and  to  determine  the  number  of  paces  in 
103  or  10CO  feet.  This  is  done  by  measuring  a  distance  with  a  tape, 
SB.-  1000  or  2000  feet,  over  ground  representative  of  that  over  which 
the  pacing  is  to  be  done  aa£  then  walking  the  length  of  the  line 
several  timec  counting  the  number  of  paces.   The  average  number 
of  paces  in  1000  feet  will  give  a  fair  value  to  use  in  subsequent 

work. 

If  the  ground  is  not  too  uneven  or  too  steep  tne  average 

distance  obtained  by  pacing  the  lines  in  both  directions  is  a 
fairly  accurate  measure  of  the  horizontal  distance. 

(22)  CHAINING  OR  TAPLNG 

Over  level  cr  nearly  level  ground  chaining  or  taping  is 

carried  out  in  the  following  manner: 

Two  men  called  rear  and  head  chainaan,  respectively,  are 
equipped  with  a  tape,  a  set  of  eleven  chaining  pins,  and  a  line 
rod.   The  head  chaintn&n  should  be  the.  acre-  experienced  and  reliable 
of  the  two  men. 

If  a  line  rod  or  other  signal  is  necessary,  it  ic  set  im- 
mediately Dehind  the  mark  at  one  end  of  the  line  in  line  with  the 
V.TO  marks  at  the  extremities  of  the  coarse  to  be  measured.   This 


Blem.  of  Surv.  iA         Assignment  '2  page  9 

line  is,  say,  between  700  and  800  feet  long. 

The  rear  chainman  takes  his  position  to  one  side  of  the 
line  at  the  end  of  the  line  away  from  the  rod.   The  head  chainman 
gives  the  rear  chainman  the  zero  end  of  the  tape  and  unwinds  the 
tape  as  he  moves  in  the  direction  of  the  rod  until  the  tape  is 
fully  extended.   In  his  hand  he  carries  the  set  of  pins  -  these 
pins,  eleven  in  number,  are  simple,  round,  vrirs  darts  with  a  ring 
bent  on  the  upper  end.   They  are  used  to  mark  temporary  points  on 
the  ground  during  the  process  of  chaining  or  taping. 

When  the  head  chainman  has  stretched  the  tape  to  its  full 
length  he  takes  one  pin  in  his  right  hand,  holds  it  against  the 
tape  at  the  100-foot  mark,  and  places  himself  to  one  side  of  the 
line  facing  the  tape  and  holding  the  tape  tout  and  horizontal. 

The  rear  chairman  then  signals  or  directs  the  head  chs-inman 
until  the  tape  coincides  witn  a  line  between  the  marks  on  the 
ground,  flhen  the  head  chainm&n  is  on  line  the  rear  chainman 
signals  "down'1  or  "stick"  and  the  head  chaimaan  presses  the  pin 
into  the  ground  in  an  inclined  position  at  right  angles  to  the  line 
being  measured.   Vn'hen  this  is  done  and  tiie  distance  checked  he 
answers  the  rear  chainmaji  by  saying  "down"  or  "stuck". 

The  rear  chainman  then  drops  his  end  of  the  tape  and  moves 

to  the  point  just  occupied  by  the  head  chainman  and  the  head  chain- 
on  line 
man  moves  forward  to  a  new  positionxdragging  the  tape  behind  him. 

The  rear  chainman  watches  the  tape  until  the  zero  end  is  about 
fire  feet  behind  the  first  pin  set  by  the  head  ehainman.   Then  he 
calls  "chain"  or  "tape11  as  a  signal  to  the  head  chainuan  to  stop. 


TSlera.  of  Surv.  1A         Assignment  2  Page  10 

This  will  bring  the  zero  point  very  close  to  the  pin.  As  the  head 
chainman.  walks  along  the  line  he  should  "line"  the  rod  in  with  some 
mark  011  the  landscape  and  keep  this  mark  covered  by  the  rod  so  as 
to  keep  himself  nearly  on  line. 

The  process  carried  out  for  the  first  100  feet  is  repeated, 
the  head  chairman  setting  a  second  pin  to  indicate  the  end  of  the 
second  100  feet.  When  the  head  chainman  in  certain  that  the  pin 
is  properly  set  he  calls  "stack",  and  the  rear  chairman  pulls  up 
the  first  pin,  Trtiich  he  carries  forward  with  hin  as  he  moves  for- 
ward. 

This  procedure  is  continued  until  the  head  chainman,  in 

dragging  the  tape  forward,  passes  the  red  set  at  the  end  of  the 
line.   This  indicateg  that  the  last  measurement  is  less  than  a 
full  tape  length.   II  the  tape  is  graduated  to  tenths  or  hundredths 
of  a  foot  throughout,  the  rear  chainman  places  the  zero  end  of  the 
tape  at  the  last  pin  set  and  the  head  chainman  movss  back  along 
the  tape  until  he  is  opposite  the  mark  at  the  end.  of  the  line. 
The  graduation  on  the  tape  iamfcdiately  over  the  nark  is  observed, 
and  to  get  the  full  length  of  the  line,  this  length  is  added  to 
100  times  the  total  number  of  pins  placed  in  the  ground  by  the 
head  chainaan.  3.  3-.  -  if  the  line  is  765.4  feet  long  there  will 
have  been  7  pins  set  in  the  ground,  six  of  which  are  in  the  rear 

i  ^ 

chaiaraan's  hand  and   one  remaining  in  the   ground,   65.4  feet   being 
the   fractional  tape   length  last  measured,   hence:. 

(100  x  7)   -f  65.4  =  7S5.4  feet. 


Hera,    of  Siirv.  Lu  Assignment   2 

In  most  cases  the  tapes  are  constructed   »itii  the   first  foot 
and  last  foot  divisions  only,   graduated  to  tenths  of  a  foot,  while 
the  main  portion  cl  tne  tape   is  graduated  to  feet.      When  this  con- 
dition exists  the  rear  chairman  holds  the  zero  end  of  the  tape  at 
the   last   pin  set  until  the  head  chairman  determines  the  position 
of  the  nearest  full  foot  ;aark  beyond  the  mark  at  the  end  of  the 
line.      The  head  chairman  then  holds  this  foot  mark  at  the  end  of 
the,-   line  while  the  rear  chainman  pulls  the  tape  backward  until  it 
is   stretched  taut.      The  distance  from  the  first  foot  marl:  to  the 
pin  is  noted  asad  gives  the  fraction  of  a  foot  to  be  added  to  the 
length   indicated  by  the   foot  mark  held  by  the  head  chainman  minus 
one  foot.      To  illustrate   -   if  the  distsvnce  from  the   last  pin  to 
the   end  of  the   line   is  65.4  feet,  the  nearest  foot   mark  beyond  the 
end   of  the    line   is   66.0  feet.      -his  point   is  tlien  held   on  the   end 
of  the   line   and  the  tape  pulled  back  until  the   C.6  foot  nark  is 
opposite  the  pin  near  the  rear  chainman  or  0.4  foot  back  from  the 

1.0  foot  marK.      tnue: 

66.0  -  1.0  +  0.4  =  65. -i  feet 

A  new  tape  made  by  the  Lufkin  Rule  Company  is  made   101  feet 
long,   having  t'.vo  feet  at  the  zerc  end  of  the  tape  graduated  to  tenths 
of  a  foot  e.nd  the   zero  point  placed  at  the  middle  point  of  these 
two  feet.      The  tenths  aariced  on  the  first  foot  run  backward  from 
the  zero.      This  type  ;aakes  the  above   arithmetic  process  unnecessary. 

The  procees  of  neasurement   just  explained  is  for  tape 
neasurenientE,   though  it   is   applied  to  measurements  with  £.  surveyor's 
or  an  engineer's  chain.      The  sole  difference   is   in  the   units  employed 


Eletn.  of  Sur-v.  1A         Assignment  2  -^age  12 


and  the  accuracy  possible.   With  the  chain  measurements  are  seldom 
taken  closer  than  to  the  nearest  one-tenth  of  a  link. 

.-Should  the  line  be  longer  than  1000  feet  the  work  continues 
in  the  uianner  outlined  until  the  head  chairman  has  placed  the 
eleventh  pin  in  the  ground.  He  then  signals  the  rear  ohainman 
for  pins  and  the  rear  chairman  comes  forward  with  ten  pins  in  his 
hand.  The  rear  chairman  carefully  counts  the  pins  and  the  head 
chainnan  makes  an  independent  count  to  check  the  tally  of  the  rear 
chainman.   If  these  counts  agree  the  rear  chainman,  as  recorder, 
marks  100C  feet  in  his  fieldbook.   i'he  eleventh  pin  marks  the  po- 
sition of  the  first  hundred  feet  on  the  next  thousand  feet  to  be 
measured  and  will  subsequently  be  counted  in  the  tally  of  the 
second  group  of  pins. 

A  method  used  by  seme  surveyors  is  to  start  the  rear  chain- 
man  with  one  pin  in  his  hand  the  the  head  chainman  with  ten  pins. 
Thus,  the  pin  in  the  rear  chainman'  s  hand  records  or  tallies  the 
first  hundred  feet  measured,  the  second  pin  the  second  hundred 
feet  measured,  etc.,  until  the  last  fractional  tape  length  is  de- 
termined.  The  rear  chainman,  in  this  method,  counts  only  those 
pins  he  holds  in  his  nend  and  does  not  include  the  last  pin  in  the 
ground.   It  will  be  seen  that  in  the  measurement  of  lines  over 
1000  feet  long  the  tally  of  pins  at  the  1000-foot  point  will  be 
the  same  in  either  method  used.  Both  methods  are  good,  the  one 
employed  being  a  matter  of  choice  on  the  part  of  the  surveyor. 


Elem.    of  £arv. 


Assiyvnent   2 


Page  13 


(23)  HORIZONTAL  UEASOBBUaft  OK  SLOPING  GiKXJHD 

This  is  much  more  difficult  of  accomplishment.   In  addition 

to  the  tape,  chaining  pins,  and  rod,  each  chainman  should  be  sup- 
plied with  a  plumb-bob,  the  string  on  the  same  to  be  about  seven 
feet  long. 

Let  it  be  desired  to  measure  the  length  of  the  line  JiB  from 
A  to  B  down  the  slope,  Fig.  1. 

The  rear  chainman  takes  his  place  at  A  as. in  the  example 
below,  while  the  head  chainman  moves  cown  the  slope  until  he  stretches 
the  tape  out  to  its  full  length. 


These  pins  re- 
turned to  head 
chainman  at  end 
of  first  100.0  fe 


100.0 


fhis  pin  retained  until  end  of  line 
is  reached. 


et. 


Fig.  1. 


&e  then  movep  back  up  the  slope  to  a  point  like  a,  a  full  number 
of  feet  from  A,  a  being,  chosen  at  such  a  distance  from  A  that  it 
•will  be  possible  for  the  head  chainman  to  hold  the  tape  horizontal. 


Blfcin,    o?  Surv..  L:.  Afsigniar.no   2  ta-^e   14 

Say  the  distance  along  the  tape  is  35.0  fset.      At  this  point  the 
head  chainman  passes  the  siriug  of  the  plumb- bob  over  the  tape   and 
allots  the  plumb-bob  to  drop  until   it    is  a   short   distance  above   the 
ground  while  the  tape   is  held  horizontal.      The  tape  is  brought  to 
the  horizontal   Oy  estimation,    Oy  comparison  with  horizontal   lines 
in  buildings  nearby,    or  by  use  of  the  hand   level.      The  rear  chain- 
majr.  holds  the   zero     end  of  the  tape  at  A  and  lines  the  head  chain- 
ii:  -    in.     iShen  the  approximate  position  of  the   point  is  determined 
a   space  should  be  cleared  of  grass  and  debris  and  smoothed  off  so 
that   t  c lear  mark  can  be  made. 

The  rear  chainman  checks  alignment  and,  when  the  plumb-bob 
cornea  to  rest,    gives  the  usual  signal.      £he  head  chainman  releases 
the  plumb-bob  vhich  v.-ill  make  a  mark  in  the  Around  directly  under 
the  35.0  foot  mark  on  the  tape.      Ihe  pluab-bob  is  removed  from 
the  mark  on  the  ground  and  a  pin  inserted  in  its  place.      (Where 
hard  ground  is  encountered  the  plumb- Dob  must  be  carefully  lowered 
tc  the.  point  to  be  established  and  a  scratch  made  with  the  pin 
which  is  then  laid  on  i-he  ground,   point  toward  the  mark.) 

1'he  rear  chaining  then  moves  forward  to  the  point   occupied 
by  the  head  chainman  and  takes    the   foot-mark  held   by  the  head 
chainman,    i.    e.    the   35.6  ft.   nark,   v;hile  the  head  chainman  noves 
further  down  the  slope  to  a  new  point  b,saj-   50.0  feet  away  on  line. 
The  mark  on  the  taps    is  noted  to  be  85.0  feet. 

The  rear  chainman  holds  the  35.0  foot  mark  e.t  the  pin  first 
set  by  the   head  chainman  and  the  head  chainman  places  a   pin  in  the 


Elem-  of  Evitv.  1-j.         .aesignaent  2  Page  15 

ground  under  the  35.0  foot  mark  in  a  manner  similar  to  that  used 
in  placing  the  first  pin. 

The  rear  chairman  again  lao-ses  forward  Ts-ith  the  first  pin  in 
his  hand  and  takes  the  85.0  foot  mark  froa  the  head  chairman.   The 
head  chain-ian  moves  do'.vn  the  slope  to  the  end  of  the  tape  and!  a 
point  is  set  under  tre  100  ft.  mark  on  the  tape.   It  is  thus  pos- 
sible to  sum  up  mechanically  the  several  short  lengths  of  tape  used 
and  to  tally  full  hundreds,  without  much  danger  of  arithmetical 
mistakes. 

The  rear  chairman  moves  forward  to  the  pin  marking  the  100.0 
foot  point  on  the  ground  '.There  he  hande  the  two  intermediate  pins 
to  the  nead  chf-inman  who  then  mores  forward  along  the  line  dragging 
the  tape  out  until  the  zero  and  is  at  the  first  100.0  foot  pin. 

This  method  of  measurement  is  carried  out  until  the  line  is 
measured.  The  last  fractional  pr.rt  of  a  tape  length,  i.  e,  the 

portion  from  c  to  3  in  the  figure,  is  determined  as  in  the  case  of 

level 
measurement  of  the  last-  iracticnal  tape  length  on  A  ground.  The 

length  is  finally  determined  by  counting  the  pins  representing  the 
full  hundreds  of  feet  ?n<?  adding  to  100  times  this  number  the  frac- 
tional length  last  obtained. 

The  measurement  of  horizontal  distances  up  the  slope  can  be 
m?.<5e  by  having  the  rear  chairman  hold  the  plumb-boo  over  the 
points  in  succession  and  the  head  chairman  move  to  points  such 
that  the  tape  can  be  held  horizontal  by  the  rear  chainman.   To 
measure  downhill  is  a  more  accurate  procedure  than  to  measure 
uphilj.,  owing  to  the  greater  difficulty  in  the  latter  case  experisnced 


;J 


4 


t 


•« 


5 


4 


I  M  5 

:IF 


i 


^F 
(* 

^ 


s 


23t/K> 


IZif. 


j 


•p«r 


^ 


if 


£_ 


.    of   Surv. 


Assignment   2 


Page  16 


by  the   rear  chainraan  in  trying  to  hold  the  plumb-bob  over  an  es- 
tablished point  on  the  ground. 

Where  uneven  ground  is  encountered  it   is  sometimes  necessary 
for  both  chairmen  to  use  plumb-bobs  to  make  it  possible  to  keep  the 
tape   straight  an  d  horizontal,   e.    g.    -a  stump  may  be  on  line  or  a 
smell  hunmock  nay  lie  between  the  e;rlreuiities  of  the  tape. 

(24)    SLOIE  iaEASUKEMLNTS  FCR  lE'fLK&INiyG  HORIZONTAL  DIST^CES 

These  measurements  nay  be  made  in  two  ways,     both  are  rather 

laborious  and  expensive,    involving  the  use  o£  ths   level  in  one  case 
and  of  the  transit    in  the  other. 


1  A 


Fig-    2. 

In  the   first  method  stakes   are  set  along  the    line  at    inter- 
vals  less  than  a  tape    length  and  the  difference   in  elevation  in 
feet   is  determined  betv/een  successive   stake  tops  by  levelling, 
the  distances  on  the  slope  between  successive  stake  tops  are  then 
measured.      From  these  measurements  the  hypotenuse  and  the  vertical 

leg  of  a  right  triangle  will  be  known. 

By  geometry  there  results  -   in  general  -  see  Fig.    2 
h  =  J  sz  -  v2        t (1) 


Elem.    of  Gurv.    1A.  Assignment  2  P^ge  17  ^ 

h  being  the  horizontal   distance,   e  being  the  slope  measurement  and 
v  the  difference  in  elevation  of  the  two  points. 

Solving  for  each  partial  horizontal  distance  and  summing 
the  quantities,   the  total  horizontal  length  will  be 

H  =  hj  +  hg  +  h^  -t- -i-  hn (2) 

In  cases  where  the-  differences  in  elevation  between  successive 
points  are  small,  an  approximation  to  the  right  triangle  formula 
will  be  found  quite  accurate  enough  and  simpler  to  use.   This 

formula  is  derived  as  follows: 

From  Eq.  (1)  raay  be  written 

V2  =  62  -  h? 

the  second  term  may  be  factored  making 

v2  -  (s  +  h)  (s  -  h) 

Since   s  and  h_  are  nearly  the  same   length  if  JP  is   small.,   assume 
that  they  are  equal  and.  apply  this  assumption  to  the  first  paren- 
thesis,    only,   calling  them  both  s. 

Then  v^  =  2s   (s  -  h) 

v^ 

Vvhaics  s  -  n  =  — - — 

Zl 

2 
and  h  =  s   -  _Z —  . (3) 

2s 

The  accuracy  of  this  formula  ms-y  be  seen  for  the   extreme 
case  where  e  -  100.000  feet  and  v  =  15.000  fest.      Ihe  accurate 
solution  g,i-vo£  h  -  So. 86^  feet  while  the  approximate  formula 
gives  h  •=  93.876  feet,   this  difference   oeing  well  withiii  the  com- 
mon limit  of  allowable  error,    e.   g.    -  1  part   in   10,000. 


Elen..    of  Surv. 


Assignment   2 


18 


To  find  the  horizontal  method  by  the  second  method  stakes 
are  set  along  the  line  in  the  same  manner  and  the  vertical  angles 
measured  with  a  transit.  These  vertical  angles  are  measured  from 
the  horizontal  line  through  one  stake  to  the  sloping  line  drawn 
from  the  same  stake  t,o  the  next  stake  on  line,  see  Fig.  3.   These 
angles  are  represented  as  o^,  o^,  c<5>  o<4,  etc.   fhe  slope 


distances,  sj_,  sg,  53,  etc.  ,  are  measured. 


Fig.  5. 
the  relation  of  parts  in  a  right  triangle  it  follows 

that      i^  =  s^  cos  o^j  (4) 

and  H    =  h]_  -t  hg  •»-  h?  +  . . .   +  hn (2)  as  above. 

Where  snail  angles   are  encountered  and  the   slide  rule  is  to 
be  used  it  is   often  convenient  to  use  the  following  formula: 

h^  -   5^  --  s^  vers   o<  i    (5) 

The  chief  advantage  in  the  use  of  this  formula  lies  in  the 
smaller  number  of  significant  figures  necessary  in  obtaining  the 
same  accuracy  as  with  the  cosine.  "Wherever  a  table  of  natural 
cosines  is  available  it  is  very  simple  to  obtf.in  the  versed  sine 


Elem.    of  Sur?.  1^.  Assignment   2  i^-ge   19 

by   remembering  the   relation 

versed  sine  =  1  -  cosine. 

This  method  ie  also  good  for  solutions  involving  arithmetical 
computations  with  natural  functions. 

INSTRUCTIONS  CCNCELKEG  SOLUTIONS  CF   PROBLEMS  AND  IHBIR 

At  the  end  of  each  assignment  a  group  of  problems  is  placed 
7,-hich  you  are  to  solve.      These  problems  will  embody  the  principles 
set  forth  in  this  and  the  preceding   assignments,     liiihen  you  solve 
these   problems  they  nraet  be   returned  P.S  evidence   of  your  mastery 
of  the  matter   in  hnnd.     VJhen  the  problem  group  has   been  examined 
r<.nd  errors   indicated,   it  will   be  graded  and  returned  with  copies 
of  the  correct  solutions  attached  for  your  comparison. 

The  solutions  of  problems   should   ue  \vor.-:ed  out  upon  the 
special  paper  furnished  ay  the  associated  Students'    Store,  Berkeley. 
All  solutions  are   supposed  to  be  your  original  work,   not  neat 
copies   of  wor£  don.:   on  other  p.per.     All  numerical  work  end,  des- 
cription Must  _be    siiCTv^i  in   i-ik. 

A  probl«n  sheulc   'of    solved  in  tuclv  a  manner  that  each  ttep 
•will  appear   ">n  the  problem  sheet  (liiinor  arithmetic  processes  and 
interpolations  exc-'ctea).      Tabulate  3.   series  of  related  partial 
or   similar  results. 

Sketches  or  diagrams  should  be  mace  to  illustrate  the   problem 
whenever  possible.      These-   sketches  inrxy  be  sn.de   in  pencil,   but  all 
lettering  and  dimensions  rust  be  shown  in  ink.      In  aaking  sketches 
reasonable  proportions  should  bt  observed  and  these    should 


Blem.  of  Surv.  1A.         &esi-.nr«nt  i;  Pa^e  20 

approximate  the  conditions  given;  it  is  not  necessary,  however,  to 
drav,-  sketches  or  figures  to  sce.le,  except  -.Then  specially  directed 

tc  do  so. 

Keatness  and  .general  arrangement     of  parts   of  a   problem 
must  be  considered.      You  should  lay  out  tine  method  of  procedure 
before  starting  to  solve  a  ^r  olden  and  then  work  out  each  step  in 

a   logical    order.      Five  aim-fees  spent  in    "blocking  out'!  the  -work 
will  save  rruch  labor  and  vrorry.      A  surveyor  should  learn  to  De 
accurate  and  as  direct  as  possible,  since  most  of  his  work  is  of 
s  nature   requiring  much  time   in  execution  and  accuracy  in  results. 
%  Problems  will   be  graded  en  neatness,  arrangement,   complete- 
ness,   and  correctness  -  each  part  of  the  above   list  holds  a  -weight 
of  one-fourth   of  the  total  grade  possible. 

References  ; 


y,  pp.  31  -  38. 
Breed  &  Hosner,  pp.  11  -  15,  vol.  I. 
Johnson,  pp.  5  -  10. 

Raymond,  p>  13  -  22. 


Elem.    of   Eurv.  1A  Assignment   2  jfege  21 


PROBLEMS 

1.  £.  man  paces  a  giver,  line  in  both  directions,   ihe  pedometer 
carried  lay  him  records  1355  paces  in  one  direction  and  1560 
in  the  other.   If  his  pace  is  30  inches  long,  what  is  the 
length  of  the  line  (a)  in  feet?  (b)  ir.  rods?   (c)  in  miles? 
(d)  in  metres? 

2.  The  horizontal  distance  between  tv,-o  points,  A  and  B,  is  desired. 
Beginning  at  A  the  course  was  divided  into  the  secTions  A-l,  1-2, 
£-3,  3-B  and  the  corresponding  quantities  E  and  v  measured,  in 
feet. 

Section     s     v       — v^_     h      E 

2s 


A-l 

98.76 

5.63 

1-2 

99.00 

10.70 

8-8 

97.42 

7.11 

3-B 

67.10 

3.24 

Compute  the  several  horizontal  distances,  h,   and  the  total 
length  H,    to  the  neereet  one-hundredth  of  a  foot,  using  approximate 
formula,      ^abulete  results. 

3.    To  find  the  horizontal  distance  between  two  points,  A  and  3, 
slope  distances   and  corresponding  vertical  angles  we're  measured. 

Section  s  cos.     method     Vers-     method 

h  H          h  H 

A-l  73.65     5° 10' 

1-2  98.65   10°56' 

2-?          100.05   26°4C' 
3-B  85-00  31°00! 

(a)  Solve  for  ths   ssveral  quantities,   h,   by  the  formula   in- 
volving the  cosine.      Jee   5-place   logarithmic   tables  and    logarith- 
mic functions.     Give  results  to  nearest   one-hundredth  of  a  foot. 

(b)  Solve  for  the  serial  quantities,  h,   by  the  versed  sine 
formula,    in  eac'u  cc.se  do  not  use  ;aore  than  three    significant 
figures   iii  the  ->ersec,  sine,   e.    £.    -  0. C0373,    0.0985,    or  0.173. 
use  natural  functions  end  solve  arithmetically. 

(c)  Tabulate  the  two  sets  of  results  and  find  H  froir.  each  set. 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 
Correspondence     Courses 

Surveying-La.  Elements   of  Surveying  Swafford 

Assignment   3 

ERRORS   IN   LINEAR  MEASUREMENTS 

FOREWORD  : 

In  this  assignment  it  is  intended  to  give  an  elementary 

outline  cf  the  errors  occurring  in  linear  measurements,  their 

sources,  their  correction,  and  their  avoidance. 

(25)  TKL  TRUE  LENGTH  Of  A  LINE 

The  true  length  of  a  line  can  never  be  definitely  known 

from  measurements  made  by  human  agency.   Mathematically  it  is  pos- 
siole  to  state  that  a  line  is  a  definite  length,  ag.  -  a  line  may 
be  said  to  be  25  feet  long,  and  from  the  purely  mathematical  con- 
sideration this  line  may  be  considered  just  25  feet  long,  no  more 
and  no  less,  out  snould  a  line  of  unknown  length  be  measured  Dy 
any  means  available  to  the  human  race  the  length  may  be  found  to 
be,  probably,  25  feet  plus  or  minus,  a  length  due  to  some  error 
which  in  the  last  analysis  will  be  indeterminable.   The  magnitude 
of  the  error  depends  upon  several  factors,  some  of  which  may  be 
dealt  with  definitely,  while  others  are,  in  the  main,  irremediable. 

(26)  ERROBS 

Errors  may  arise  from  two  general  sources,  namely,  imper- 

feet  ion  of  instruments,  and  imperfection  of  the  human  functions. 


the  first  head  ma,,  be  listed,  the  erroneous  length  of 
a  chain  or  tape,  change  of  length  due  to  a  rise  or  fall  of  temper- 
s/tare, irregular  graduation  of  tape  or  otner  scale,  ncn-adjustment 


.  oi'  Surv,  1;.         ..iSSign^e-rit  3  ^age  2 


of  instrument,  arid  such  injuries  to  equipment  as  the  kinking  of  a 
tape  or  chain  and  the  Sending  of  spindles  or  compass  needles. 

The  effect  of  human  imperfection  is  shown  in  several  ways. 
Meet  of  the  errors  arising  from  this  condition  are  termed  personal 
errors   This  general  group  may  be  again  divided  into  what  are 
called  mistakes  and  accidental  errors. 

Mistakes  are  errors  that  occur  in  the  mind  of  the  observer, 
as,  the  v,rong  foot  mark  -.vill  be  read  from  the  tape;  an  angle  of  52 
degrees  r.-ill  be  read  as  57  degrees;  in  long  lines  a  tape  length 
will  be  lost  or  added;  in  attempting  to  repeat  an  angle  five  times, 
the  instrument  man  may  turn  off  the  angle  six  times.  When  sighting 
a  long  distance  on  a  sunny  day,  a  person  may  regard  the  bright  side 
of  a  rod  as  the  full  width.  When  this  supposed  iric'th  of  the  rod  is 
bisected,  the  line  of  sight  is  actually  to  one  side  of  the  true 
point.  Here  -y;e  have  a  mistake,  net  an  accidental  error. 

Ajccidentai  errors  are  really  small  mistakes  -  mistakes  which 
do  not  come  from  a  confusion  of  thought,  but  from  the  imperfection 
of  human  sight  and  touch,  or  from  inaccuracy  in  estimation.   These 
errors  are  exemplified  by  the  small  errors  created  in  setting  chain- 
ing pins  or  in  estimating  fractional  divisions  on  a  tape  or  circu- 
lar scale. 
(27)  CUMULATIVE  E3KORS 

Cumulative  errors  occur  from  inperiection  of  equipment  or 
fron  known  natural  causes.   A  tape  may  be  too  long  or  too  short. 
In  the  first  case  the  measured  length  of  the  line  will  be  shorter 
than  the  true  length  by  the  product  of  the  error  in  one  tape  length 


Slera.    of  Surv.    IA  Assignrn«nt  3  Page  3. 

multiplied  by  the  number  of  times  the  tape  length  is  contained  in 
the  total   length  of  the   line.      Should  the  tape  be  too  short,  the 
reverse  would  be  true. 

The  cumulative  errors  common  to  chaining  or   linear  measure- 
ments are  : 

1.  Incorrect   length  of  tape  or  other  measuring  device. 

2.  Change   of  temperature,    above  or  below  the  standard. 

5.    Incorrect  alignment,    i.e.,  both  aids  of  tape  not  held 

in  a  horizontal  line  or  in  the  vertical  plane  including 
the  ends  of  the   line  measured. 

4.  Tape  not  stretched  straight  and  taut  but  with  the  ends 

etill  on  the   line. 

5.  Sag  of  the    tape  due  to  wind  or   lack  of  proper  tension. 

(28)   CCUSTABl  JSJD  VARIABLE  ERRORS 

Conulative  errors  may  be  divided  into  two  sub-classes, 
constant   *nd  variable  errors.      There  is   but  one  constant  error, 
that  due  to  the  erroneous   length  of  tape.     All  of  the  other  cumu- 
lative errors  are  generally  variable  in  their  nature.      Temperature 
is  constantly  changing;  the  same  errors   in  alignment  are  not    likely 
to  be  repeated;  the   sag  of  the  tape  will  vary   according  to  the  ten- 
sion in  the  tape.      It   is  possible  that  the   sag  and  the  temperature 
effects  will  be  constant  under  soae  conditions  and  therefore  cause 
constant  errors.      Likewise  the  pull  applied  at  the  ends  of  the 
tape  sine  to  a  misunderstanding  of  what  the  proper  tension  should 
be,   may   be   in  error  by  a   constant  amount. 

Accidental  errors  are  in  their  nature  variable. 


El  em.  of  Surv.  lA      Assignment  3  Page  4 

(29)  CORRECTION  OF  TIE  MEASURED  LENGTH  OF  A  LINfc 

The  correction  for  the  several  kinds  of  cumulative  errors 
be  determined  by  considering  the  nature  of  each  error,  its  law, 
and  its  magnitude.  While  under  certain  conditions  accidental 
errors  follow  a  precise  law,  it  is  impossible  to  correct  them  by 
mathematical  means.   The  only  way  to  eliminate  them  is  to  adopt 
such  methods  as  will  make  the  possibility  of  such  errors  as  small 
as  possible.   It  is  evident  that  they  can  not  be  entirely  avoided. 

(30)  CORRECTION  FOR  FALSE  LENGTH  OF  TAPE 

The  false  length  of  a  tape  may  be  due  to  several  causes. 
In  the  process  of  manufacture  the  attempt  ie  made  to  make  the  tape 
Just  IOC'  feet  long  when  the  temperature  is  62  degrees  Fahrenheit, 
the  pull  12  pounds,  and  the  tape  fully  supported  on  a  flat  surface. 
This  ideal  result  is  seldom  if  ever  realized;  hence  the  tapes  pur- 
chased from  the  best  raaKers  are  usually  slightly  in  error. 

After  long,  continued  use  the  tape  is  liaole  to  be  kinked 
in  several  places.  If  the  kinks  have  been  straightened  the  tape 
will  probably  be  too  long  because  of  the  permanent  stretching,  of 

the  material  .   if  the  :cinxs  Jnj\e  not  been  removed  the  tape  will 
probably  be  toe  short. 

A  tape  way  be  broken  and  subsequently  patched.  TShen  broken 

a  portion  of  the  t??e  may  be  lost;  or  the  tape  may  be  lapped  in 
repairing;  or,  if  a  splice  be  made,  the  t\vo  snds  of  the  break  may 
not  be  brought  into  proper  contact.   This  source  of  error  in  the 
length  of  the  tape  is  one  that  should  be  carefully  considered  in 
each  individual  case,  for  the  greater  portion  of  the  tape  may  be 


Elen.  of  Surv.  Lt        Assignment  3-  Page  5 

reasonably  correct  vrhile  the  error  at  the  patch  will  affect  only 
such  measurements  as  shall  include  this  part.   It  should  be  noted 
here  that  an  apparently  perfect  tape  or  one  with  kinks  in  it  may 
have  greater  error  in  one  part  than  in  another. 

An;  one  or  all  of  these  conditions  may  occur  in  one  tape. 

In  a  chain  there  is  the  possibility  of  the  long  links  be- 
coming kinked  and  thus  making  the  chain  too  short.   On  the  other 
hand,  there  is  a  possibility  of  the  many  oval  limes  and  the  rings 
at  the  ends  of  tl'e  long  links  becoming  stretched  or  of  the  surfaces 
of  contact  between  theia  beconing  so  worn  that  the  chain  will  be 
elongated.   It  will  be  remembered  that  a  chain  hag  over  600  wearing 
surfaces.   The  adjustable  handles  at  the  ends  of  the  chain  are  used 
to  correct  the  total  length  of  the  chain  but  it  evidently  does  not 
follow  that  such  a  means  will  correct  fractional  measurenents. 

If  a  tape  is  shorter  than  standard  the  measured  length  of 
the  line  will  be  too  great..   If  the  tape  is  longer  than  standard 
the  meapurec  length  of  the  line  will  be  too  small.  By  this  is 
meant  that  a  tape  nominally  100. CO  feet  long  and  so  assumed  in 
raaking  t.he  measurement  will,  in  the  first  instance,  be  contained 
a  greater  nuinbtr  of  times  in  the  total  length  of  the  line,  and,  in 
the  second,  a  lesser  number  of  timss  that  would  a  tape  of  standard 
length.   (It  should  be  observed,  th&t  the  measured  length  of  a  lint 
ie  a  ratio;-  the  length  of  tape  to  length  of  line. ) 

There  are  two  general  cases  which  arise  in  this  connection, 
one  where  the  error  in  the  length  of  the  tape  io  uniformly  distributed 


Blem.    of  Surv.    1>_  Assignment  3  Page  6 

throughout  the  tape,  ,?  nd  another  •srhere   the    error   is   located  at  a 
certain  place   in  the  tape. 

In  the  first  case  a  simple  mathematical   relation  may  be   set 
up  between  the  false  and  the  correct  values  by  considering  what 
he.s  been  said  before.      This  may  be   stated  as  follows  : 

lf    ;   Lf  =  10    :   Lc   .......  (6) 

or,  put  into  words: 

The  false  (nominal)  length,  of  tape  (If)  is  tc  the  measured 
length  of  the  line  (Lf)  as  the  correct  length  of  tape  (lc)  is  to 
the  c  or  re  c  t  length  of  t  he  1  ine  (  Lc  )  . 

LC  it  the  correct  or  adjusted  length  of  the  line,  Lr.  is  the 
measured  length  of  the  line,  10  is  the  correct  or  standard  length 
of  the  tape  and  If  ie  the  false  (nominal)  length  of  the  tape. 

From  (6)  may  be  written 

L,  = 


For  example,   assume  that  a  line  has  been  measured  with  a 
taps  nominally    100.  jO  feet   long  and  that  when  the  tape  has  been 
corapared  with  a  standard   it   is  found  to  be  actually  99.95  feet 
long,  the  error  uniformly  distributed.      The  total  measured  length 
of  the   line  is  375.66  feet.      Substituting  in  (7) 


r     =  _.  =  375.47   feet. 
100.  00 

In  the  case  where    the   error  ia  concentrated  at  one  place  in 
the  tape  the-  proolein  is  carried  out  in  the  following  manner  : 

First:     Determine  the  magnitude  of  the  error  and  the  portion 


Elesi.  oi'  Surv.  !«.         Assignment  3  Page  7 

of  the  tape  in  which  the  error  exists,  i.  e. ,  in  the  first  ten 

feet,  in  the  vicinity  of  the  fifty-foot  raark,  etc.   Call  the  error  e. 

Second:  Measure  the  length  of  the  line  in  the  usual  manner, 
using  the  nominal  length  of  the  tape.   Note  at  the  last  measurement 
whether  or  not  that  portion  of  the  tape  is  used  that  contains  the 
error. 

Third :  Count  up  the  number  of  full  tape  lengths,  each  one 
of  which  is  known  to  contain  the  total  error,  and  call  this  number  N. 

Fourth :  If  the  last  fractional  measurement  involves  the 
error,  add  one  unit  to  JS  making  the  number  (N  +  1).   If  the  last 
fractional  measurement  does  not  include  the  error  add  nothing  to 
N  ("this  also  applies  if  the  last  measurement  is  a  full  tape-length 
and  follows  from  the  third  step  above). 

JTiftJri:  From  the  foregoing  can  be  written 

Lc  =  Lf  +  e(N  +  1)  (8) 

in  the  case  where  the  error  occurs   in  the   last  measurement. 

Or  Lc  =  Lf  ±  eN      (9) 

when  the   lest  measurement  does  not  contain  the  error. 

lo  illustrate   (8)  :     Suppose  that  the  measured  length  of  the 
line   is  375.36  feet   and  that  the   length  of  the  tape  ie  99.95  feet 
by  a  comparison  with   the  standard,    though  nominally  100.00  feet 
long.      Let   it  further  be  assumed  that  an  error  of  0.05  foot  occurs 
within  the  first  75  feet  of  the  tape.      Then, 

Lc  -  375.66   -  0.05  (3  +  1)   =  375.46 

To  show  the  effect  when  the  error   is  not  in  the   last  measurement, 


Elem.    of  Surv.  lA  Assignment  3  P^ge  8 

let  it  be   assumed  that  the  error  of  0.05  foot  appears   in  the  last 
20  feet,    all  other  conditions  being  the  same  as  above,      fhen. 

L     =  375.66   -  0.05   (5)   =  375.51  feet. 

c 

,  The  pluc-or -minus   signs  in  (8)  and  (9)   indicate  that  the 

tape  may  be  either  too  long  or  too  short   and  the    correction  is  to 

be  applied  accordingly. 

(31)   CORRECTION  FOR  CHANGE  IK  TEMPERATURE 

The  standard  temperature  for  most  steel  tapes  is  eet  at  62 

degrees  Fahrenheit.      Sines  temperatures  vary  from  day  to  day  and 
from     one  hour  of  the  day  to  another,    it  is  a  common  phenomenon 
that  a  tape  changes   its   length  accordingly.      Most  steel  tapes 
expand  or  contract  at  the  rate   of  O.OOG0063  to  0.0000065  of  their 
length  for   every  change  of  one  degree  Fahrenheit  (this  quantity  is 

4 

a  ratio  ard  is  called  the  coefficient  of  expansion;  see  any  text 
on  Physics).   Assuming  the  temperature  of  all  parts  of  the  tape  to 
be  the  same  at  any  one  time  the  change  of  the  length  of  any  portion 
of  the  tape  "7ill  be  proportional  to  the  eh?nge  in  temperature  and 
to  the  length  of  the  tape  involved. 

If  it  is  assumed  that  T  is  the  standard  temperature  for 
the  tape  and  that  T  is  the  temperature  or  the  tape  at  tne  tiae  of 
measurement  of  a  distance,  also  that  one  nominal  tape  length  is 
measured,  i.  e,,  100. OO  feet, 

10  -  If  ±  0.0000065  lf  (T  -  I8)  ...  (10) 

The  plus-or -minus  sign  indicates  that  the  correction  be  added  when 
the  temperature  is  higher  than  standard   and  vice  versa. 


Elem.  of  Surv.  1A        Assignment  3  Page  9 

It  will  be  noted  that  if  the  temperature  is  higher  than 
standard  the  tape  will  be  too  long,  hence  it  will  be  contained 
too  few  times  in  the  length  of  a  line  measured  under  these  con- 
ditions.  In  other  words  the  line  appears  too  short,  hence  the 
principle  set  forth  in  (10)  holds  for  the  measured  length  of  the 

• 

line  and   it  may  be   stated 

Lc   =  Lf  ±  O.OOC0065  Lf   (T  -  Tg)    ...    (11) 
Ihw  same  rale  regarding  signs  holds   as  for  (10). 

In  making  this  correction  it  must  be   recognized  that  the 
temperature  will  in  all  probability  vary  considerably  daring  the 
work  of  measurement.      The  usual  practice  is  to  take  the  tempera- 
ture for  each  tape   length  measured,  to  correct  each  tape   length, 
and  then  to  find  the  total  distance,  though  in  certain  types   of 
v;ork  the   several  temperatures  are  averaged  and  the  average     ie 
used  in  the   application  of  the  formula  to  the  full   length  of  the 
Ij  ne. 

As  an  illustration  of  the  method  assume  that  the  measured 
length  of  the   line  is   375.66  feet,   and  that  the  average  temperature 
ie  78  degrees  Fahrenheit.      Substituting  in  (11) 

Ls  -  375.66  +  (O.OOOuOSd  x  37s. 66   (78   -  62;)   =  375.70  feet. 
It   is   evident  that  a  minute   error  -will  be   introduced  by  using  the 
false   length  of  line  or  the  nominal  length  of  the  tape,   but  this 
error  is  so   srnali  tiiat  it  may  safely  be  neglected  in  most   surveying 
work* 


,    cf     bur".  1A  assignment   3  Page   10 


(32)  CORHLCT1CN  FOR  Eitf.OHS   DT  A 

ferncujr*  in  niiynw««ij  (mould   w*  *%«».*•*,    out  wh«»«  iupU  *  thing 

as   intentional   deviation  f*om  the   straight    line   is   necessary,   use 
should  "oe  nade   of   (3).  AS  £i  grime  :it  II,   page   17.      The  distance,    in 
this  case,    sboula  be  measured  on  the  hypotenuse   of  tht   right  tri- 
angle and  the  perpendicular  distance  from  the    line  to  the  end  of 
the  tape   should  lie  the  short   leg  of  the  triangle.      This  correction 
is   o'uviously  i'or   only  those  measurements  en  each  side  of  the  ai&rK 
vhere  the  end  of  the  tape  is  off  the   line,    and  for  no  others. 

(33)  CC3ELCiIOBi  FOE  T^-ffi  NOl   S^KitiT  AKD  twill 

Errcr  in  this  cise  i^ia^    bt  prevented  jy  proper  care   in  seeing 

that  the  tape  is  straight  and  taut. 

(34)  GORI-SCTIOi-   FOk   iAG  OF  XrtPE 

When  tL  cord  cr  strip  of  material  of  uniform  cross  section 
and  of  perfect  flexibility  is  supported  in  a  horizontal  position 
by  suspension  from  two  points  it  assumes  a  curved  form  in  a  ver- 

tical plane.      This  curve  is  called   a  catenary;   and  it    is  possible    . 

• 
tc  compute  its  foam  mathematically.     But  since  the  equation  of  the 

catenary  is  awicvrard  to  use   in  general  work,   an  approximation  is  nade 
"u;y  assuming  that  the  curve  is  a  paraoola.      Ihis  assouiptxon,   not  go 
rauch  in  error  as  might   oe  imagined,   gives,    on  th^e  v/hole,  a  very 
satisfactory  solution  of  the  problem. 

Professor  R.    3.  'woodward  derives  the  final  equation  for  the 
correction  of  length  of  a  tr.pe    in  the  u.    &.   Coast  and  geodetic  our- 
vey  Report  of  1S92.      ihie  equauion  must  be  accepted  as  correct  un- 
til you  have  haa  a  thorough  trainirig  in  Calculus  end  Engineering 
Mechanics. 


Eleau  of  Surv.  1A         Assignment  3  Page  11 

This  final  form  for  tne  difference  in  span  for  the  tape 
fully  supported  and  for  the  tape  supported  at  the  ends  only,  may 
be  written  1   /  vl\ 

°s  :  IT  \T)    (12) 

Equation  (12)   is  the  correction  for  &  full  tape   length 
•when  supported  at  the  two  ends  of  the  tape.      cs   is   the  correction 

for  the  full   span  given  in  the   same  units  as  1;    1  is  the  total 

i 
length  of  span  in  feet;  w  is  the  weight  of  the  tape  in  pounds 

per  linear  foot;  ana  p  is  the  pull  in  pounds  applied  at  the  ends 
of  the  tape.  This  equation  will  also  apply  for  any  sp?.>n  of  the 
tape  less  than  full  length,  if  the  spaa  is  substituted  for  1. 

If  the  tape   is  supported  at  several  points  we  must  consider 
the   sag  effect  per  span.      In  such  case  the  tape   is  divided  into, 
say,  ri  spans  of  3c  feet  per   span.      If  n  =  1, 

2 


(13) 


Sag  tends  to  shorten  the   span  of  the  tape  and  causee     the 
measured  length  of  the   line  to  be  too  long,    i.e.,   the  tape  is  con- 
tfined  too  many  times  in  the  line  measured.      The  correct   length 
of  the   line   is  expressed  by  the    fomula 

IfcStf-.Cj (14) 

Cg  in  (14)  is  the  summation  of  the  several  quantities  cg 
found  for  the  several  tape  lengths  measured.   If  ii  tape  lengths, 
including  the  fractional  tape  length  at  the  end  of  the  line,  be 
taken,  then 

C.  -  cs  •*•  c-  +  cs  -f -f  cs  •"  (15) 

s    S     s     s  s      v  i 


Elesi.    of  Surv.  IA  ^eignment  3  Page   12 

One  -should  not  fall   into  the  error  of  assuming  that  the 
several  quant  itiee,   cs,   can  be  multiplied  by  N  except  under   special 
conditions;  for  an    inspection  of  the   formula  will  indicate  that  the 
correction  in  each  c&se  depends  upon  the  cube  of  the  span,  the 
number   of  epane   into  which  the  tape   is   divided,   and  the  pull  on 
the  tape,  all   of  which  may  vary.      The  weight   is  usually  constant 
for  the  tape  used. 

Let  the   length  of  the  line  measured  be   375,66  feet,  the 
pull  applied  at  each  tape   length  measured  be  ,20  pounds,  and  the 
weight  of  the  tape  per   linear  foot  be  0.010  pound.      The  assumption 
is  that  the  conditions  in  each  of  the  first  three  hundred-foot 


measurements  are  the   sr.aie.      Then 

x          .  2 

-  0.0104  foct. 


LOO.  00    •    0.010  x  100.  00 


62 

For  the   last  75.66  feet,   however, 

75.  G6     0.010  x  75.662 


From  the  above, 

cs  =  0.0104  +  0.0104  +  0.0104  -f  0.004-5  ~  0-0357  foot. 

and 

Lc  -  376.66  -  0.036  -  3^5.  6£  feet  (to  nearest  O.ul  foot), 


Ag^in,  the  nominal  length  ia  used  but  the   error  is   so  slight 
as  to  be  negligible. 

The  srror  caused   oy  tie    lateral  sfc.^  cf  the  tape    .;nder  vine 
prc-s&are   is  so  variable  that   it  is   impossible  to  correct  it.      The 
effect  of  wind  is  to  shorten  the  tape   auct  iaake  the  measured  length 
cf  the   line  too  long.      The   only  tning  to  do  when  the  wind  is  blowing, 
sufficiently   strong  to  cause  a  large   error  is  to  stop  'ffork  until 
conditions  will  allow  good  work  to  Oe  done. 


t    of  isurv.    l.-x  Assignment,  5  Page   13 

QUESTIONS 

1.  In  measuring  a  line  what  four  sources  of  error  are 
liible  to  occur?  ' 

2.  Explain  the  difference  in  method  of  applying  error  in 
length  of  tape : 

(a)  'When  the  discrepancy  is  uniformly  distributed? 
( o)  When  discrepancy  is  due  to  a  defect  in  one  part  of 
the  tape  only. 

3.  Miy  are  measured  distances  made  by  leveling  the  tape? 
What  other  means  may  be  used  to  accomplish  the  same  object? 

4.  Distinguish  between  an  error  and  mistake  in  taking 
measurements.   When  may  a  mistake  be"  called  a  blunder? 

5.  Kow  may  pacing  be  used  as  a  check  on  blunders  in 
measurement  of  a  line? 


OF  CALIFORNIA  EXTENSION  DIVISION 
CORRESPONDENCE- STUDY  COURSES  IN  TECHNICAL  SIBJECIS 

Course  1A  Elements  of  Surveying  Swafford 

Assignment  4 

ERRORS  IN  LINEAR  MEASUREMENTS 
(continued) 

FOREWORD : 

This  assignment  is  a  continuation  of  the  discussion  of  errors 
in  linear  measurements  with  particular  eaphasis  on  accidental  errors 
and  the  law  governing  them.  A  later  portion  of  the  assignment  is 
devoted  to  a  discussion  of  precision,  discrepancies,  and  allowable 
errors. 
(35)  ACCIDENTAL  ERRORS 

Accidental  errors  h&ve  a  tendency  to  balance  each  other; 
they  are  often  called  compensating  errors.   It  is  unfortunate  that 
this  term  has  been  used,  for  it  tends  to  mislead  a  person  into 
believing  that  by  some  magic  or  other  the  effect  of  accidental 
errors  is  eliminated  in  all  cases.   In  the  greater  part  of  the 
work  done  in  surveying  each  quantity  is  measured  but  once,  and 
furthermore,  moat  quantities    measured  are  relatively  small. 
KShere  the  relatix^ely  small  quantity  is  measured  many  times  or 
where  large  measurements  are  made  so  tnat  tnere  will  be  many 
partial  measur events  every  accidental  error  will  have  a  tendency 
to  bal  ance  some  other. 

A  mathematical  study  of  the  law  of  errors,  particularly 
accidental  errors,  and  the  probability  of  errors  (see  Merriman's 
"Method  of  Least  Squares")  shows  that  such  errors  will  come  nearer 
and  nearer  to  balancing  each  other  as  the  number  of  meaeurements 


Elem.  of  Surv.  IA       Assignment  4  Page  2 

approaches  infinity.  This  meane  not  that  in  the  measurement  of  a 
single  tape  length,  for  instance,  the  accidental  error  will  be 
eliminated  out  that  the  total  length  of  a  line  measured  by  repeated 
trials  approaches  more  nearly  the  true,  unknowable  length,  the 
greater  the  number  of  times  the  line  is  measured. 

It  must  not  be  supposed  tnat,  if  a  ion£  line  is  measured 
by  a  great  number  of  partial  measurements,  the  total  length  will 
be  more  accurately  determined  than  the  length  of  a  shorter  line 

of  fewer  partial  measurements  made  with  the  same  care  and  under 
the  same  conditions.  On  the  contrary,  the  actual  error  will  in 
all  probab  ility  be  less  in  the  shorter  line^ 

The  common  accidental  errors  occuring  in  linear  measurements 
are  caused  by 

1.  Variation  of  pull  or  tension  in  the  tape. 

2.  Error  in  setting  pins  or  other  markers. 
Kiet&kes  or  blunders  may  occur  through 

1.  Incorrect  count  of  tape  or  chain  lengths. 

2.  Mistakes  in  reading  the  graduations. 

3.  Disturbing  of  pins  or  other  markers  after  chey  have 

been  set. 

(36)  CORRECTION  OF  ACCIDENTAL  ERRORS 

Of  all  the  accidental  errors  lifter5  the  only  one  Trhich  may 
be  corrected  mathematically  is  that  due  tc  variation  of  pull  or 
tension.  This  error  lies  on  the  border  line  between  a  true  cumu- 
lative error  and  an  accidental  error,  due  to  the  fact  that  in  moat 
surveying  the  pull  is  estimated  and  not  exactly  measured. 

The  case  does  arise,  however,  where  the  pull  ie  measured 
with  a  dynamometer  or  spring  balance.  When  this  is  che  case  the 


Eleir.-  of  Surv.  IA        Aceignment  4  page  3 

effect  of  pull  coraes  into  the  group  of  cumulative  and  correctable 
errors. 

It  has  been  found  that  if  a  bar  of  steel  one  square  inch  in 
cross  section  r.nd  of  any  length  1,  is  stressed  by  applying  loads 

at  the  ends  of  the  bar,  the  bar  will  be  either  stretched  or  shoi-tened 

1 

by  •"'""'•-  ',•;.•     of  its   length  for  ever./  pound  of   load  applied.      Hence 
3G,OOC,vA>0 

if  the  area  of  cross   section  of  the  tape   and  the  .nagnitude   of  the 
pull   applied  are  !<nov:n 

CP  =  ~1S~~  (16) 


This  is  a;i  expression  of  Hooke's?  Law  (ees  Church's  "Mechanics 
of  Engineering")  in  which  _£  is  the  pull  applied  in  pounds,  I  the 
length  of  the  apan  of  the  tape  used  in  feet,  A  the  area  of  crocs 
section  of  the  tape  in  square  inches,  and  E,  the  modulus  of  elasticity 
(30,000,000  pounds  per  square  inch).,  c  Till!  then  be  given  in 
fractions  of  a  foot  f^r  all  cases  that  arise  in  surveying, 

If  in  pleasuring  a  lina  the  pull  is  determined  for  each  tapt 
length  or  fraction  thereof,  the  corrected  length  will  be  found  from 


Cp  is  the  summation  oi"  all  the  quantities  o  ,  the  sane 
principle  applying  as  in  the  correction  for  sae;.   it  should  be 
noted  that  while  it  is  usual.  ly  necessary  to  compute  the  pull  cor-  . 
rection  for  each  separate  tape  length  we&sured,  taere  are  many 
cases  in  which  it  is  proper  and  tetter  to  correct  the  whole  length 
of  the  line  at  one  time. 

To  illustrate  this  le^  it  be  assuvned  that  the  length  of 
line  measured  is  375.56  feet,  pull  on  the  tape  23  pounds,  crose 


Elem.  of  Sarv.  IA        Assignment  \ 

section  of  the  tape  0.0029  square  inch,  E  •-  30,000,000  pounds  per 
square  inch,  and  that  the  nominal  length  of  the  tape  ifc  100.00 
feet.   It  is  further  assumed  that  the  same  pull  is  exerted  for 
each  tape  length  or  fraction.  Then 

CP  °  Tsx&rnis&txas  =  °-08:3  or  °-09  f6et' 

and 

L     -  375.36  +  C.OS  -  375.  75  feet. 
c 

pull  always   lengthens  a  tape  and  no.  ice  5  the  correction  addi- 
tive.     A  cojanon  case  that  arises  is  where  a  tape  is  found  to  be 
juet   100.00  feet  long   ander  a  certain  tension.      If  the  pull  be 
below  that  assumed  as   standard,  the  correction  v.-ill  bo  negative  for 
the  difference   in  length     found  by  computing  the.  correction  for 
each  tension.      This   is  but  a    step  from  the  above  method. 

(37)   NORMAL  TENSION 

If  the  two  corrections,    sag  and  pull,  are  made  equal,    it 

is  possible  to  simplify  the   later  computations  by   obtaining  v<hat 
ie  called  normal  tens  ion.      Hence  placing 


Pi  -    . 

_AE  "  24p 


the  normal  tension,  p  =        ................  (18) 

V  24 

If  the  \alue  of  p  is  found  for  a  temperature  of  62  decrees  Fahrenheit 
so  as  to  make  the  tape  span  just  what  the  true  length  of  the  tape  is 
when  fully  supported  and  unstressed,  the  taring  in  work  will  be  con- 
siderable. A  table  or  diagram  may  be  constructed  for  a  particular 
tape  such  that  the  normal  tension  for  £ny  span  of  the  tape  may  be 
quickly  obtained. 


Elem-  of  Surv.  lA        ^ssigrinent  4  Page  5 

The  normal  tension  above  must  not  be  confounded  with  the 
so-called  normal  tension  which  will  make  the  span  of  the  tape  just 
100  feet  when  supported  at  the  two  ends,  for  in  the  latter  case 
the  pull  and  sag  will  probably  not  balance  each  other,  because  the 
tape  may  not  be  just  100  feet  long  v.-hen  unstressed  and  fully  sup- 
ported. 

(38)  PRECISION 

While  all  surveying  should  be  conducted  with  due  care,  all 

surveys  need  not  be  made  with  the  same  precision,  and  precision 
in  some  parts  of  a  given  survey  should  be  more  scrupulously  sought 
than  in  other  parts.  The  purpose  of  the  eurvey,  the  time  or  its 
equivalent,  the  money  expended  in  doing  the  work,  will  and  should 
in  a  measure  determine  the  refinement  of  methods  and  the  character 
of  instruments  employed.  For  example,  a  compass  and  chain  survey 
suffices  for  the  ordinary  uses  of  farm  or  timber  lands,  or  for 
estimating  crops,  areas  ravaged  by  fire  etc.,  while  the  measuring 
out  of  a  city  lot  would  call  for  a  transit  and  tape  eurvey  pos- 
sibly to  the  last  refinement.   In  the  determination  of  a  Base  Line 
(see  Johnson,  pp.  447  et  seq. )  not  only  is  evex-y  step  made  with 
extreme  care,  but  every  known  source  of  error  in  measurement  is 
considered;  corrections  are  applied  for  alignment,  sag,  pull, 
temperature,  and  difference  in  level;  and  finally  a  reduction  to 
sea-level  is  made,  and  many  checks  and  balances  are  sought. 

In  railroad  surveys  the  different  degrees  in  precision  may 
be  aptly  illustrated  by  the  methods  employed  in  the  various  steps, 
as  for  reconnaissance,  preliminary,  and  location,  while  also  in 


Elem.  of  Surv.  IA        Assignment  4  fage  6 

the  last,  location,  different  degrees  are  further  observed  for 
separate  parts  of  the  wor*. 

In  cases  where  two  or  more  determinations  of  the  same 
measured  quantity  are  made,  any  large  discrepancy  should  be  re- 
jected and  a  mean  of  the  fairer  values  taken.  This  does  not  imply 
that  a  mean  of  two  or  more  observed  values  is  correct,  but  that 
the  possible  error,  too  large  in  one  case,  is  balanced  by  a  pos- 
sible error,  too  small  in  another.  While  this  is  not  necessarily 
true,  for  both  may  oe  too  large  or  both  toe  small,  it  is  regarded 
as  a  safe  course  to  pursue  where  each  value  is  determined  with 
equal  care.  Furthermore,  discrepancies  serve  to  indicate  mistakes, 
the  most  common  source  of  wide  discrepancies. 

Ordinarily  a  tape  that  is  known  to  be  standard  may  be  relied 
upon  for  most  work.  The  distances  measured  on  slope  and  reduced  to 
level  may  also  be  relied  upon  when  the  inclination  is  exactly 
Known,  fhe  character  of  the  territory  traversed  -  hillj,  7/ooded, 
or  marshy  -  calls  for  varying  degrees  of  precision;  it  is  not  well 
to  apply  methods  of  refinement  inconsistent  with  the  nature  of  the 
land,  if  it  is  sufficient  that  the  survey  be  correct  in  the  ratio 
of  I  in  200,  it  vould  be  folly  to  try  for  correctness  in  the  ratio 
of  1  in  5,000,  or  10,000  or  more.  Consistency  is  the  essential 
element  always. 

No  error  known  to  exist  should  be  permitted  where  it  may  be 
removed.   If  a  traverse,  for  example,  does  not  close  by  an  amount 
that  seriously  affects  the  result,  some  lines,  or  angles,  must  be 
remeasured  to  determine  the  discrepancy. 


Elem.  of  Surv.  1A        Assignment  4  Page  7 

Ideal  conditions,  such  as  measurement  over  open  territory 
on  firm  and  level  ground  are  seldom  realized.  When  such  conditions 
do  not  obtain  the  surveyor  must  exercise  great  pains.  A  disregard 
of  reasonable  means  to  secure  fair  results  is  inexcusable.  Over 
wooded  areas  man/  obstructions  such  as  trees,  brush,  etc.  are 
present,  wnich  must  be  removed  anless  corrections  are  applied  to 
each  tape  length  or  line  segment.  «ere  the  knowledge  we  may  have 
of  the  nature  of  the  obstruction  must  govern  the  result,  or  the 
judgment  of  the  chairunen  must  be  called  upon. 

It  is  often  necessary  to  pass  some  such  obstruction  as  a  tree 

h2 

standing  upon  the  line;  in  such  case  the  correction  c  =  -sr  is 

cii 

necessary.      This  correction  must  be  subtracted.     Here  h  is  the  off- 
set from  the   line  at  the  point  where  it  occurs  and  L  ie  the  length 
from  the  point  on  line  to  the  offset. 

On  slopes  the  tape  should  be  carefully  Isveiec,  preferaoly 
•with  a  tape-level  or  by  aid  of  a  hand-level  (to  be  described  later 
on  in  the  assignment,  on  Leveling)  and  the  end  points  of  the  tape 
should  be  tiansf erred  tc  the  ground  by  aeans  of  plurcb-bob.     Where 
great  precision  is  not  required,   the  tape  may   be   leveled  with  the 
eye,    lining  it  in  by  the  horizon  or  the   lines   of  a  building.     A 
rude  substitute  for  the  plumb- bob  is  a  chaining  pin  dropped  from 
the  point  to  the  ground.      Caution  must  be  used  in  chaining  on 
slopes,   as  these  often  appear  greater  than  they  really  are.      In 
ascending  a  slope  it   is  more  likely  to  misjudge  than   in  descending. 
In   "breaking"  tape  do  not  make  the  blunder  of  mistaking  the  wrong 
division  nark. 


• 


Elea.  of  Surv.  i&        Assignment  4  page  8 

The  errors  common  to  chaining  may  now  be  summarized..   These 

are : 

Error  in  Tape  -  longer  or  shorter  than  standard.      If  longer, 

the  measured  line  is  too  short;  add  a  correction.      If  shorter,  the 


measured  line  is  loo  long;   subtract  a  correction. 


h2 


Error ,   tape  not  horizontal  -^  the  correction  -rr-  must  be 
subtracted. 

Error  due  to  temperature  -  if  temperature  is  above  standard, 
tape  is  too  long,  correction  must  be  added;  if  below  standard,  cor- 
rection subtracted. 

Error  due  to  tension  -  if  pull  is  below  normal,   line  too 
short;    add  correction;   if  pull   is  above  normal,   subtract  correction. 

Error  due  to  JBJ;  is  a  cumulative   error  that  must   be  corrected 
by  adding  a  calculated  quantity. 

Error  in  al ignment  is  synonymous  with  that  for  tape  not 
horizontal. 

Do  not  make  blunders,   such  as  reading  the  wrong  tape  divi- 
eion,  plumbing  down  from  th3  tape   ends,  making  wrong  count   of 
tape-lengths,   or  disturbing  pins  when  once  set. 

References : 

Tracy,   pp.    39  -  46. 

tfreed  &  Hosiner,   pp.    11  -   13 ,  vol.    I. 

pp.    24  -  33,   vol.    II. 
Johnson,   p.    449  et   seq. 
Raymond,   pp.    25  -  30. 


UNIVERSITY  05'  CALIFOKrt.Lk  EXTENSION  DIVISION 
COBRESPOKDEHCB-afODr  COURSES  IN  TfcCiiKIC/i  SUBJECTS 

Course   !U.  Elements  of  Surveying  Swafford 

Assignment  5 
THE  COMPASS  A.KD  ITS  USES. 

FOREWORD : 

This  following  assignment  outlines  the  terms  used  in  compass 

of 

•urvityiag  and  gives  a  description  the  compass  and  ite  usa. 

(39)   THE  MAGNETIC   NEEDLE 

The  peculiar  properties  of   the  magnetic  needle  afce  known 
in  a  general  way  by  nearly  everyone.      This  needle  is   a  slender  bar 
of  iron  which  has  been  n.agnetised  and  suspended  upon  a  pivot   so 
that   it  may  swing  freely    in  n.  horizontal  plane  and,  within  a  limit- 
ed amount,   vertically. 

If  tike  needle  is  allowed  to  swing  freely  it  will   soon  come 
to  rest,   pointing  in  a  northerly  direction.      Should  it  be  disturbed 
and  again  allowed  to  come  to   rest  it  will  be  found  to  point  in  the 
Bane  direction  as   it  did   in  the  first  instance.      This  is  due  to  the 
fact  that  the   earth  is  a  great  toagnet  with  a  positive   or  north 
pole   in  the   region  of  the  geographical  north  pole  and  a  negative 
or    south  pole  in  the  region  of  the  geographical  south  pole. 

The  end   of  the  needle  which  points  to  the  north  magnetic 
pole  of  the  earth  is  the  negative  end  of  the  needle.     This  end 
is  called  the  North  end  of  the  needle  because   it  always  points 
toward  the  north  magnetic  pole.      This  north  end,   in  the   surveyor's 
compass  cew   be  easily  distinguished,   for   in  the  north  latitudes 
the  south  end  of  tije  needle  has  either   z.  small  brass  sleeve  or 


..   cf     Surv.    1A  Assignment  5  Page  2. 

a  wrapping  of  fine  brass  wire  fastened  about  it   bttveen  the  pivot 
and  the  extremity. 

(40)  THE   DIP  OF  XHE  kA&WIIC   NEEDLE 

The  wrapping  of  wire   is  necessary  on  account  of  the  dip  of 
the  magnetic  needle.     Tfllhea  Li^netized  the  uorth  end  wings  toward 
the  north  magnetic   pole  and  in  doins  so  is  drawn  downward  so  that 
the  needle  assumee  a  final  position  in  T,rhich  the  north  end   is  much 
lower  than  the   south  e:icu      This  dip  is  zero  at  the  Equator  and  in- 
creases until  the  needle   stands   in  r,  vertical  position  at  a  point 
just  north  of  Eudeon'fl  Bay.      In  a  similar  manner  the   south  end  of 
the   needle  will   dip  for  positions  south  of  the  Equator.      The 
wrapping  or   erase  wire   is  used  as  a  counterweight  v/ith  which  to 
balance  the  needle. 

(41)  THE  iiAfiKETIC   POLKS  OF  THE  EARTH 

The  magnetic  poles  do  not  coincide  with  the  geographical 
poles.      The  geographic  poles  are  the  two  points   on  the  earth  where 
the  axis  of  rotation  pierces  the  surface,     fhe  north  magnetic  pole 
liee   just  a  short  distance  north  of  Hudson's  Ba^  ,   Canada,  while 
the  south  ma0netic  F°ifc   ^-r-  ^st  south  01  .australia,      in  general, 
then,   the  magnetic  needle  does  not  point  toward  the  true  or  geo- 
graphic north  pole.      Since  the  term  north  is  used  rather  loose ly 
by  everyone,    it  will  be  well  to  give  a  clear  definition  of  the 
terms  used  in  this  discussion. 

True  or  geographic  north  or  south  will  be  indicated  by  the 
*   words    "true  north"  or    "true  south". 

Magnetic  north  will  be  called    "magnet io  north". 

North,   unqualified,  will  indicate  the   north  direction  as 


m^A^''^ 

TX'   f    /r\     ~ YTfc-J T»  .rf^'i1"^'-^*^"/ — f  c"""     ^-  -  f  r-^^JS      ~*^f-r      /"V£   "x-v  \  ^ 

I^^IC^^^r^-^- 
5^^^^:^»J%:sy^.,'''  . 


ESifeS: 

«5'>  ,  -*^ 


£Vp< 

'    ov 


K«r  A^  ,^^ 


i,«-^j 

aa^lTKCMa' 


If 


-S-1 


^l 


.:--' 


i  O'a 


^'ifeW 


-L] 

S\    r^      ^ 

^W 


^p^ 

/  v  A  7^p\^K, 


»5^/)p» 

J¥  -  (   ° 

•  ^^s^gkJ 

-v-^_'  _^ 


^z 


Xv 


,_,v-^->^-r"-7-r:  \  -.: 

SS^ 

o 


<®  to 


c\^       A    ^ 


i 


* 


«-i  B 
°e 


||, 

f  II 
|j' 

=3-1 

•Sag 

|Ja 

E  w  » 

—  o  § 

l^x 
I  SI 

!*l 

4.  "H    ^ 

-sa 

HI 
tsi 

*>5«, 

2:3" 
^5? 


•2^3 
1=f 

lil 

isi 

ill 
^•3* 

•c  c  » 

iig 


u  to 


S  *0 

M! 

.II1  i 
«l  I 

P,?     -2 


c?-5? 

O   B    3   o 

•£fS| 

ri§ 

-So^.S 

1W 

6  o  **  « 

all  a 

ll!l 

w  e "?»« 

Ill 

«^  u  § 

T-ali 

|8I] 

x||S 

se 
ii 


E'Venu  of  Surv.  I/.         Assignment  5  Page  3 

applied  in  discussions  involving  either  true  or  magnetic  north, 
the  limitation  being  set  by  the  nature  of  the  problem  end  method 
used. 
(42)  DECLINATION  OF  THE  NEEDLE 

Magnetic  surveys  of  the  earth's  surface  show  that  the 
pointing  OJL  the  needle  uoee  not  iollow  a  regular  law.   The  angle 
by  which  the  needle  points  away  from  the  geographic  or  true  north 
is  called  by  surveyors  the  declination  _o£  the  needle,  which  is  the 

same  as  the  nautical  term  Variation.   If  the  needle  points  to  the 

to 
east  of  true  north,  the  declination  is  east  and  if,, the  vest  of  the 

true  meridian,  tne  declination  is  west. 

The  declination  of  the  needle  is  different  for  different 
localities  on  the  surface  of  the  earth.  if  an  observer  traversed 
a  line  along  v;hich  the  declination  of  the  needle  is  constant,  his 
path  would  be  an  irregular  line.  This  line  is  called  an  isogonic 
line,  a.,  line  oi  constant  variation  of  declination  of  the  magnetic 
needle.  Figure  ^  is  a  chart  shoeing  ths  positions  of  such  lines 
for  the  United  States. 

There  is  P.  line  extending  from  the  region  of  Lake  buperior 
to  south  Carolina  v/hich  is  aartceti  0°.   This  is  the  Agonic  Line  or 
line  cf  no  declination.   If  the  needle  is  read  at  any  point  along 
this  line  the  magnetic  north  will  coincide  i-rith  the  true  north. 
To  the  east  of  this  line  the  declination  is  viest  and  to  the  west 
of  this,  line  the  declination  is  east. 


En.err-..    c*  Suv-t.  1...  Assignment  5  Fnge  4 

(43)   CH7WF-    I";..    DnC ...I':.*:  ION 

Th?  declination  of  the  needle  is  not.  constant.   In  fact,  the 
declination  of  the  needle  is  changing  continually. 

Secular  variation  is  a  slrv  ?hart£c  cav.psl,  apparently,  by 
the  slow  shifting  of  the  magnetic  poles  of  the  earth.:   The  law  of 
the  change  or  its  caus?  is  not  clearly  understood.   In  the  United 
States  the  change  in  declination  from  this  ccuso  is  about  three 
minutes  per  year  on  the  average.   This  change  is  not  the  sane  for 
all  localities;  the  greatest  rate  of  change  is  near  the  Agonic 
Line  and  the  rate  diminishes  as  the  distance  from  the  Agonic  Line 

increases.   Lines  indicating  the  annual  change  are  shown  on  the 
chart. 

Annual  variation  is  a  small  change  of  approximately  one 
minute  of  arc. 

Diurnal  or  Daily  "^'-r iation  is  a  change  in  the  declination 
of  the  needle  occurring  each  day.   The  anoar.t  of  the  variation 
depends  upon  the  season,  of  the  year  and  the  tiua  of  day,  r -is  3  ing 
fron  3  to  12  minutes.;.   The  needle  is  in  its  most  e?3~cerly  position 
at  about  8  a.m.  and  in  i«s  most  westerly  position  at  aoout  1:30  p.m.; 
the  mean  positions  occur  at  sbout  10  F...m..  ar.d  t:Z-0  n-"1' 

Irregular  yarintions  cone  from  a  variety  of  causes  such  as 
electrical  or  magnetic  storms,  during  which  tnc  .noveaents  of  the 
needle  are  so  erratic  that  it  is  impossible  to  read  it  accurately 
and  from  local  attraction,  which  will  .cause  a  definite  deflection 
of  the  needle. 


Elem.  of  Surv. 1A         Assignment  5  Pag&  5 

Of  the  variations  in  declination  the  most  important  are 
the  Secular  and  Diurnal  Variations.  The  Annual  Variation  is  so 
small  that  it  is  unimportant.   In  the  case  of  Irregular  Variation 
due  to  magnetic  storms,  etc.,  all  that  can  be  done  is  to  wait 
until  the  disturbance  subsides.   Local  attraction  is  easily  cor- 
rected in  most  cases. 
(44)  THE  SURVEYOR'S  COMPASS 

The  surveyor's  corr.ppss  is  a  deviee  for  obtaining  the  di- 
rection of  lines.  A  compass  box  is  mounted  on  a  vertical  spindle. 
The  spindle  turns  in  a  hollow  vortical  sleeve  at  the  lower  end  of 
•which  is  a  ball  and  socket  joint.   The  whole  is  mounted  upon  a 
tripod  so  that  the  instrument  may  be  set  firmly  over  a  point. 

The  tripod  is  provided  with  a  loop  or  hook  immediately 
under  the  center  of  the  vertical  spindle  so  that  a  plumb-bob  may 
be  suspended  from  it  while  setting  the  instrument  up  over  a  point. 

The  bottoir.  of  the  compass  box  is  a  dial.  In  this  dial,  or 
art  the  frame  carrying  the  dial,  are  two  sm«.ll  spirit  levels  which 
are  set  parallel  to  tl.e  bottom  of  the  compass  box  and  therefore 

perpendicular  to  the  vertical  axis  of  the  instrument;  one  level 

These  are  used  in  leveling  the  dial. 
ie  parallel,  the  other  perpendicular,  to  the  line  of  sight.  A  The 

dial  is  divided  into  quadrants,  one  end  of  the  line  being  marked 
N  or  with  sorae  conventional  device  to  indicate  north.  Diametrically 
opposite  is  placed  S  for  south.  The  ends  of  the  line  at  right 
angles  to  the  first  line  are  marked  E  and  W. 

On  a  circle  which  is  raised  a  short  distance  abo-ve  the 
dial  are  found  the  graduations,  usually  degrees  and  half  degrees. 


..    •  .  ••• 

-    -     . 


-  •     . 


''••••'..I.-':       ••-••. 

••'."•  .  '  ,-.•:'•• 

' -  '•  '  •'       '••-...       "  .'. 


El  em.  of  i>urv.  IA        A&siganent  5  Page  6 

At  the  point  corresponding,  to  north  end  to  south  the  graduations 
are  narked  0°,  while  the  points  E  and  W  are  marked  90°.  The  inter- 
vening divisions  are  conveniently  marked  in  tens  so  that  readings 
may  "be  easily  made. 

On  the  frame  carrying  the  compass  box,  or  on  the  sides  of 
the  compass  box,  are  mounted  two  standards  or  sights.   These  are 
vertical  bars  several  inches  high  in  which  narrotv  slits  are  cut 
for  sighting.   la  certain  types  of  compass  there  are  just  two  nar- 
row slits,  while  in  others  there  is  a  very  narrow  slit  in  one  stand- 
ard a$d  a  wider  slit  in  the  other  standard  in  which  is  mounted  a 
fine  wire  or  thin  metal  strip.   These  standards  are  fastened  to 
the  compass  box  on  the  line  marked  K  and  S,  which  line  is  the  line 
of  sight  of  the  instrument. 

in  the  center  of  the  compass  box  is  a  fine,  needle-like 
pivot  on  which  the  magnetic  needle  swings,   i'his  pivot  is  very 
carefully  centered  and  should  be  handled  delicately.   On  this 
pivot  swinge  the  needle,  supported  on  a  jewelled  bearing  similar 
to  the  bearing  on  the  balance  wheel  in  a  watch.   The  jewel,  either 
of  glass  or  of  some  serai-precious  stone,  is  mounted  at  the  center 
of  the  needle  in  a  circular  setting.   It  has  a  small  conical  de- 
pression cut  in  it  into  which  the  pivot  fits. 

The  «rhole  needle  mechanism  is  very  delicate;  hence  a  lever 
is  placed  in  the  lower  portion  of  the  compass  box  by  means  of  which 
it  is  possible  to  raise  the  needle  off  the  pivot  while  the  instru- 
ment is  being  moved  from  one  place  to  snother. 


E^em.  of  Surv.  LA.         Assignment  5  Page  7 

The  compass  box  is  covered  with  a  thin  sheet  of  glass  to 
protect  the  delicate  parts  within  from  dust  and  damage. 
(4-5)  BEARING  OF  A  LINE 

In  surveying  with  a  compass  the  angular  quantities  deter- 
mined by  means  of  the  compass  itself  are  called  bearings.   The 
bearing  of  a  line  may  be  defined  as  the  angle  which  the  line  makes 
with  a  line  of  standard  direction  called  a  meridian  (i.e.  either 
magnetic  meridian  or  geographical  meridian). 

Bearings,  either  true  or  magnetic,  are  reckoned  from  the 
north  to  the  east  or  west,  and  from  the  south  to  the  east  or  west. 
As  stated  above,  the  graduated  circle  of  the  compass  is  narked 
from  0°  at  N  and  £  to  90°  at  E  and  W,  hence  bearings  range  from 
zero  degrees  to  ninety  degrees  only.  To  illustrate: 
N  0°  E  (or  70;  N  15°  W;  S  8SC  E;  S  11°  W. 

Where  the  bearing  is  exactly  K  or  S  or  E  or  IV,  it  may  be  so  indi- 
cated by  usihg  for  brevity  the  single  letter,  but  .it  often  prevents 
confusion  to  indicate  auoh  a  bearing  as  in  the  first  exanple  above. 
Bearings  are  never  more  than  80°  from  the  N  or  S,  respectively. 

The  bearings  are  determined  by  the  position  of  the  needle 
with  reepect  to  the  markings  on  the  dial,  and  by  the  position  of 
the  line  sighted.  Usually  magnetic  bearings  are  obtained.  These 
may  be  subsequently  changed  to  true  bearings  if  the  magnetic  dec- 
lination is  known  for  the  time  and  locality  (see  Computation  of 
Angles  and  Bearings,  Art.  54,  Assignment  VI).  A  mechanical  de- 
vice known  as  a  declination  arc  is  found  on  some  compasses,  by 


Blem.    of  Surv.  IA  ^.ssjg.nnent  5  Pag-e   8 


means   of  which  iA   5.s  possible  to  set  the  compass   circ.le   so  as   to 
obtain   the  _t£ue  bearing  directly,    (See  Leolinaticai  AT?..,   Art.    48.) 
TO   GST  UP  A  COMPASS 

To  set  up  a  compass  over  a  point  ,   the  procedure   is  as  follows 

1.  The   instrument  ioan  stands  the  cciapass  before  him  so  that 
the  two  legs  of  the  tripod  are  toward  him  and  the  third  leg  away 
from  him. 

2.  He  grasps  the  two  nearer  ]  sgs   in  one  hand  and  the.  third  • 
leg  in  the  other,    strings  the  th5rd  leg  a-.»ay  from  him  till  the  angle 
between  the   legs  is  about  30°,   places   tha  foot  of  the  leg  on  the 
ground  about  three-  feet  beyond  the  point   over  which  the  instrument 
is  to  oe   set,  and  plants   it  firaly. 

» 

3.  He  then  takes    ihe   other   legs,   one  in  each  hand,  amd 
swings  the  whole   instrument  and  tripod  toward  him,    opening  the 
legs  of  the  tripod  c.s  he  does  so,   until  the  center  of  the  tripod 
ie  approximately  ovtr  ths  point   on  the  grcuud   and  the   le^s  c,bout 
eynniet-'ically  placed.      Th^   legs  are  then   set   on  the  ground. 

4.  The  plumb-bob   is  then  suspended  from  the    Ijcp  on  the  tri- 
pod.     In  doing  thin  c-".xe   is  taken  to  tie  a    "running  bcw  knot"  in 
the  string  sufficiently  far  below  the  loop  so  thaj:,  the  liei^ht  of 
the  plumb-bob  above  the  ground  may  be  regulatsd. 

5.    H«  determines   the  position   of  the  pj.urab-bob  with  reepect 

about 
to  the   point  on  the  ground  and  moves  the  feet   of  the  tripod/\until 

the  plumb-bob  hangs  directly  over  the  point.      Thiu   shifting  requires 
considerably  practice  before  the  surveyor  becomes  adept  at   it. 


Elsm.  of  Surv.  IA        Assignment  5  Page  9 

5.   lo  level  the  instrument  he  grasps  the  compass  box  or 
frams  (never  the  standards)  firmXy  in  both  hands  and  tilts  the 
head  of  the  instrument  about  the  ball  and  socket  joint  until  both 
small  bubbles  in  the  level  tubes  remain  in  the  center.  As  a 
cautionary  measure  it  will  be  well  to  bring  one  bubble  to  the  cen- 
ter of  ita  tune  at  a  time.  He  swings  the  head  about  the  vertical 
axis  until  the  bubble  tubes  are  turned  180°  from  their  former  po- 
sition and  notes  whether  the  buobles  remain  in  the  center.   If 
they  do  not  he  brings  each  bubole  half-way  back  toward  the  center 
of  its  tube,  making  the  dial  of  the  compass  level  and  the  vertical 
axis  truly  vertical.  The  reason  for  this  will  be  apparent  after 
the  Adjustment  of  the  Level  Tuoes  has  been  read. 

7.  He  releases  the  needle  by  means  of  the  lever,  and  allows 
it  to  swing  fresiy.  The  instrument  is  then  ready  for  use. 
47)  TO  TAKE  THE  BEARING  OF  A.  LINE, 

The  instrument  Oeing  set  up  over  one  end  of  a  line,  it  is 
possible  to  obtain  the  bearing  of  the  line  as  follows: 

1.  The  needle,  for  any  locality,  points  in  a  fixed  direction, 
namely,  toward  the  magnetic  pole.  (Magnetic  north.) 

2.  The  line  of  sight,  as  determined  oy  the  slits  in  the 
standards,  swings  about  the  vertical  axis  past  the  needle. 

3.  The  dial  with  graduated  circle,  rigidly  fastened  to  the 
standards,  swings  about  the  vertical  axis  under  the  needle. 

It  must  be  Kept  clearly  in  mind  that  the  needle  is  sta- 
tionary for  any  one  ''set-up"  and  that  the  dial  end  the  line  of 
sight  move. 


E.Um.  cC  Surv.  IA 


10 


In  placing  th-3  3  and  W  on  the  dial  their  positions  are 
r*-."srrfia  from  the  ^aot  wid  west  points  of  the  horizon.  This  fol- 
lows directly  from  the  three  considerations  ircaediately  above  and 
will  be  clear  after  a  reference  to  Figures  5  and  6. 

True 

ngrth    ^  magnetic 

north 


graduated 
circle 


Fig.  5 


-  6 


Figure  5  shov/s  the  compass  box  set  so  tiiat  the  line  of  sight 
points  toward  the  magnetic  north,  in  which  case  it  coincides  with 
direction  of  the  needle.   The  magnetic  declination  is  taken  as 


E'.em.  of  Surv,  l£        Assignment  5  Page  11 

17°  19'  East  arid  is  so  shown  on  the  figure,  i.  e^,  nagnetic  north 
is  east  of  the  true  north. 

To  obtain  fehe  bearing  of  e.  15  re,  sight  en  a  signal  at  the 
far  end  of  the  line  from  •where  the  instrument  is  set  up.   Sighting 
consists  of  turning  the  compass  DOX  until  the  slits  in  the  standards 
are  in  the  same  vertical  plane  witn  the  line  on  the  ground,  that  is, 
ths  signal  will  appear  in  the  middle  of  the  farthest  slit  or  will 
be  covered  by  the  metal  strip  in  tnat  slit  when  sighting  through 
the  nearer  slit. 

Assuming  that  Figure  6  represents  these  conditions,  it  is 
seen  that  the  needle  still  points  to  the  magnetic  north  and  that 
the  line  of  sight  pointe  in  a  northwesterly  direction.   Since  the 
sero  has  moved  with  tne  line  of  sight  the  Worth  end  of  the  needle 
points  toward  a  graduation,  eay  30°  30'  from  the,  zero  but  to  the 
.Bright  or  eastward  i'raa  0°.  The  line  has  a  bearing  that  is  really 
N  30°  SO1  W.  An  examination  of  the  dial  shows  that  ths  90°  point 
in  the  right-hand  portion  of  the  dial  is  marked  W,  as  above  inai- 
cated.   It  is  now  apparent  why  the  letters  t;  and  W  are  reversed  on 
the  dial.   The  bearing  shown  is  the  magnetic  bearing  of  the  line. 
(48)  TtiL  Di/CLD'Ai'IOtt  ArtC 

The  declination  arc  is  a  device  which  makee  it  .possible  to 
take  the  true  bearing  of  a  line  directly.   This  arc  is  festened 
rigidly  to  the  portion  of  the  compass  box  which  carries  the  full, 
graduated  circle  and  extends  about  35  degrees  in  both  directions 
from  zero.   It  is  commonly  graduated  to  half  degrees.   This  scale 
is  similar  to  the  main  scale  of  the  compass. 


Elem.  of  s>'..rv.  ]A        A83«gnn«nt  5  Page  12 

Fastened  tc  the  portion  of  the  compass  box  carrying  the 
dial  is  a  small  vernier  s--:a.l3,  or  merely  an  index  line*  The  ver- 
nier scale  is  graduated  tVcm  sere.  In  the  ii> i-?.d ).e  ,  to  thirty  in 
both  directions.   (ics  .Theory  of  the  VerriJ.tr.)  3y  Eisnns  cf  the 
index  mark  or  vernier  it  is  possible  to  set  off  an  angle  on  the> 
declination  arc. 

In  Figure  5  the  declination  arc  is  shown  in  the  "North" 
position  of  the  compass  box.  The  declination  arc  ie  so  set  on 
the  compass  box  that  •when  the  zero  on  it  coincides  with  the  zero 
of  the  vernier  or  the  index  nark,  the  zero  on  the  main  circle  lies 
in  the  line  of  sight.   This  is  true  no  matter  where  the  declination 
are  may  be  fastened  to  the  compass  box. 

The  line  of  sight  is  connected  with  the  portion  of  the  box 
carrying  the  dial  *nd  vernier  or  index  mark. 

Referring  to  Figure  7  let  it  be  desired  that  bearinge  taken 
with  the  magnetic  needle  be  the  true  bearings  of  the  lines.   The 
needle  will  always  point  toward  the  magnet io  north.  From  the  fig- 
ure it  will  be  seen  t"..?t  if  the  needle  is  to  read  zero  degrees 
when  the  line  of  sight  is  pointing  torard  the  true  north  it  will 
be  necessary  to  swing  the  line  of  sight  WEST  of  the  zero  on  the 
graduated  circle.   This  is  accomplished  by  the  use  of  the  declina- 
tion arc  and  vernier.   Using  the  saae  magnetic  declination  as  be- 
fore the  setting  is  shown  in  the  figure.   The  needle  points  to 
zero  and  the  line  of  eight  points  to  the  true  north.   It  must  be 
noted  that  the  marks  indicating  the  cardinal  points  of  the  compass 


Elem.  of  aurv. 


Assignment  5 


Page  13 


True  North 


^Magnetic  North 


17°19? 


Vtrnier  roads 
17°l9r  E 


True 

K.  North- 

K    \17°19' 
30°30f 


Magnetic  North 

Beitring  (True) 
S  30°30'  E 

Bearing  (Magnetic 
17°19'  = 
*'    ~^^  S  47°49'  > 


Fig.  7 


Fig.  8 


turn  around  under  the  graduated  circle  with  the  line  of  sight  so 
that  readings  should  oe  referred  to  the  graduations  on  the  circle. 
The  markings  on  the  dial  ere  used  to  indicate  the  general  position 
of  the  line  of  sight,  only. 

This  setting  is  made  but  once  for  any  locality  and  the  parts 
should  be  clamped  securely  so  that  it  will  not  be  changed  during 
the  course  of  the  survey  in  all  cases  in  which  the  declination  arc 
is  set  off  as  explained  above. 

Figure  8  shows  the  compass  set  for  a  bearing  of  S  30°  30'  E. 
The  relative  positions  of  the  parts  of  the  compass  ^should  be 


Elera.  of  Surv.  Lfi.        Assignment  5  Page  14 

carefully  noted  and  compared with  their  positions  in  Figures  5, 
6  and  7. 

(49)  READING  TEE  COMPASS  KEEDIE 

ThiB  is  a  simple  operation,  but  it  should  be  carefully  done. 

Most  compasses  are  now  made  so  that  the  sighting  ie  done  from  the 
S  end  of  the  dial  through  the  N  end.   If  this  be  the  oase  the  north 
end  of  the  needle  should  be  read  at  all  times  to  determine  the  bear- 
ings of  the  lines  sighted.   That  is,  always  place  the  eye  in  sight- 
ing at  the  south  standard  in  whatever  direction  the  sighting  is 
made  and  read  the  graduated  scale  at  the  north  end  of  the  needle. 

If  the  compass  be  so  constructed  that  it  is  possible  to 
sight  from  either  the  S  or  K  end  the  following  rules  should  be  ob- 

•> 

served : 

1.  If  sighting  from  the  S  end  of  the  compass  through  the  N 

end  or  if  the  H  en'i  cf  the  compass  is  towerd  the  point  sighted, 

/ 
read  the  north  end  of  the  needle. 

£.  If  eight ing  fron  the  N  end  of  the  compase  through  the 
S  end  or  r..f  the  b  snd  of  thrv  compose  is  toward  the  point  sighted, 
read  the  south  erd  of  the  needle. 

In  reading  the  tearing  it  is  always  best  to  look  along  the 
needle  from  the  end  opposite  from  th-3  one  being  read.  This  prolongs 
the  line  of  the  needle  until  it  intercepts  the  graduated  circle 
and  eliminatee  parallax  or  apparent  sidevise  displacement  of  the 
needle. 

References : 

Tracy,  pp.  293  -  300. 

Breed  &  Hosner,  pp.  16  -  30,  vol.  I. 

Johnson,  pp.  13  -  57. 


Elem.    c£   Surv.  TA.  Assignment   5  Page   15 

PROBIEMS 

1.  The  magnetic  oearing  of  a  line  is  S  16°  30'  W.   The  declination 

of  the  needle  is  11°  15'  E.   Draw  n  figure  similar  to  those 
shov.ii  in  the  asoi^-uient  to  show  tne  position  of  the  coTipass 
with  respect  to  the  line  and  with  re  ape  it  to  the  true  meridian. 
Make  the  dial  three  inches  in  dianeter,  outside  dimensions, 

2.  Draw  P.  diagram  shewing  the  conpass  set  to  give  ihe  true  bearing 

of  the  line  shov.n  in  Problem  1.  TOiat  ie  this  bearing? 

3.  Draw  a  diagram  showing  the  conpass  sighted  along  a.  line,  the 

true  bearing  of  TriiicU  is  Ii  56°  W,  so  as  to  give  the  magnetic 
bearing.   I;  the  declination  is  10°  M,  what  is  this  bearing? 

4.  The  ceolination  of  the  needle  at  the  present  time  at  r.  certain 

place  is  17'  nif-  The  secular  variation  is  5'  eastward  per 
year.  What  "/ill  the  declination  of  the  needle  be  in  five 
years'; 


OF  CALIFORNIA  EXTENSION  DIVISION 


Course  1A  Elements  ol  Surveying          Swafford 

Assignment  6 
COMPAbS  KUhVEYING 

FOREWORD: 

This  assignment  deals  with  compass  surveying  methods  in- 
cluding traversing  with  the  compass,  computation  of  angles  from 
bearings,  bearings  from  angles,  detection  and  correction  of  local 
.  attraction,  and  adjustments  of  the  compass 

(50)  TEAVEHSIHG  WITH  THE  COMPASS 

The  compass  was  one  of  the  earliest  surveying  devices  used 
in  modern  surveying  for  determining  the  directions  of  lines,  and 
while  it  i«  little  used  today  except  for  reconnaissance  and  the 
checking  of  more  accurate  work,  the  method  of  traversing  with  this 
instrument  should  be  thoroughly  understood. 

Traversing  is  the  process  of  bounding  a  lot  or  field  or 
measuring  the  angles  and  perimeter  of  the  field.   In  other  words, 
it  is  the  process  of  traveling  around  the  perimeter  of  a  polygon 
in  such  a  way  as  to  determine  its  dimensions. 

There  are  three  common  cases  -which  arise  in  this  work:- 

1.  That  in  vhich  the  actual  corners  of  the  fields  may  be  oc- 
cupied by  the  compass  and  in  which  the  lines  may  be  measured  di- 
rectly. 

2.  That  in  -rhich  the  corners  of  the  field  cannot  be  occupied 
by  the  instruments,  but  in  which  the  lengths  of  the  lines  can  be 
measured  directly. 

3.  That  in  which  the  corners  of  the  fields  cannot  be  occupied 


'  '  ' 


. 


to  keep  the  rod  plumb. 


Elem.  of  Surv.  lA        /.ss.'.gnrent  6  Page  2 

by  the  instrument  and  in  which  the  lin«s  cannot  be  measured  flirectly. 

The  first  case,  which  is  ths  simplest,  will  be  explained  in 
this  assignment.   The  second  and  third  cases,  which  are  not  so  easy 
of  solution,  will  be  considered  under  Traversing,  Assignment  X, 
Art.  94. 

Kefer  to  rigure  9,  which  represents  complete  field  notes 
for  a  compass  survey  of  a  farm.   Ihe  procedure  was  as  follows: 

Beginning  at  the  point  marked  A  the  compass  was  set  up  over 
the  stake  and  properly  leveled,  The  instrument  mao  then  sighted 
at  the  point  L  and  noted  the  bearing,  U  72°  15'  E,  this  value  being 
recorded  in  the  third  column  on  the  left-hand  page  of  th^  noteoooi 
between  D  end  A-  This  bearing  is  called  the  back  or  reverse  .  oearing 
of  the  line  DA.  £r_  the  bearing  of  the  line  AD.  This  terminology 
should  be  very  carefully  noted  eo  that  the  student  will  not  be  con- 
fused in  later  discussions.   The  circle  in  the  instrument  used  was 
subdivided  into  quarter  degrees  of  15'  divisions  but  all  readings 
were  taken  to  the  nearest  5  minutes  by  estimation. 

After  the  above  reading  was  recorded,  the  instrument  man 
sighted  on  the  point  3  and  the  forward  bearing  of  the  line  AB  or, 
simply,  the  bearing  of  the  line  AB  was  recorded  in  the  second  col- 
umn on  the  line  between  A  and  B_.  A  sight  was  then  taken  on  the 
point  £  for  the  purpose  of  checking  the  work.  Ihis  bearing  was 
noted  on  the  sketc..  on  tne  right  hand  page. 

The  rodman  held  a  rod  over  the  points  D  and  A  being  careful 
to  keep  the  rod  plumb. 


Blem.    of  ^urv.    1A  Assignment  5  Page  3 

The   instrument  man  then  moved  tr  the   points  b,   C,    and  D 
respectively,  wher^  he  repeated  the  process  as  at  A.     At  the  point 
C  a  sight  was  taken  to  point  A.      ihe  bearings  read   in  each  instance 
were  recorded  in  their  proper  places   in  the  f ieldbook. 

The  distances  were  then  chained  and  recorded  in  the   sixth 
column  on  the   left  hand  page. 

The  right  hand  page   shows  a  sketch  of  the   field  which  should 
always  be  a  part  of  good  field  notes.      Such  a  sketch  should  show 

the   shape  and  dimensions  of  the  survey  approximately  to  scale,  the 

natural 
position  of  ireportant^and   artificial   features,   the    name   of  the 

owner  and  the  naiies  of  adjacent  owners,   the  meridian  (both  true 
and  magnetic   if  possible; ,    and  such  explanatory  notes  as  would 
make  the   findings   clear   to  any   later   surveyor  who  might  have   oc- 
casion to  use  them.      It    is  generally  the  experience   of  surveyors 
to  find  that  most   field   notes  are  not  full  enough.      The  tabulated 
notes  should  tally  with  the  quantities  recorded  on  the    similarly 
designated   sketch  and  should  be  similarly  designated. 

The  notes  on  the   left  hand  page  include  a  column  ior  the 
stations  occupied,    a  column  each  for  the  forward  and  reverse    oear- 
ings   of  the    lines,    a  column  ior  local  attraction,    another   for  the 
corrected  bearings,  and  one  for  the  distances.      The   lower  portion 
of  the  page   shows  the   interior   angles   cf  tbr     field   and   the   'is>iel 
check  for  such   a  survey. 

(51)   LOCAL  ATTRITION 

Local  attraction  is  the  disturbance    at  any  particular  point 


•  t. 


Elem.  of  Surv.  IA.        Assignment  6  Page  4 

or  station  which  caueea  the  needle  to  swing  out  of  the  magnetic 
meridian.   It  is  c^-sed  by  the  presence  of  magnetic  metals  nearby, 
or  by  electric  power  lines  in  the  vicinity.   The  surveyor  should 
take  reasonable  care  that  he  does  not  carry  iron  keys  or  a  knife, 
and  that  he  does  not  leave  any  portable  objects  close  to  the 
instrument,  such  as  chains,  tapes,  iron  aligning  rods,  etc.,  that 
would  disturb  the  needle.  An  annoying  source  of  variable  local 
attraction  is  found  in  steel  buttons  or  clasps  on  clothing  worn 
by  the  instrument  man  or  his  assistants. 

Local  attraction  is  appreciable  over  varying  areas  depending 
upon  the  magnitude  of  the  source,  but  it  is  usually  felt  within  a 
very  restricted  area  and  the  disturbance  decreases  as  the  distance 
increases.  The  Law  of  Magnetic  Attraction  or  Repulsion,  is  that 
magnetic  attraction  varies  directly  as  the  intensity  and  inversely 
as  the  square  of  the  distance  from  the  source. 

Where  the  local  attraction  cannot  oe  removed  the  magnitude 
of  the  disturbance  of  the  needle  must  be  determined  and  corrections 
made  in  the  notes. 

(52)  DETECT  ION  AND  CORRECTION  OF  LOCAL  ATTRACTION 

Again  referring  to  Figure  9,  columns  2  and  3,  it  will  be 
seen  that  the  forward  and  the  reveise  bearing  of  the  line  AB  are 
just  180  degrees  apart.   Thie  condition  should  hold  for  the  two 
bearings  of  any  line  surveyed  and  would  indiaate  that  there  was  no 
disturbance  of  the  needle  at  either  of  the  two  points.   It  might 
be,  however,  that  the  disturbance  at  both  of  the  points  was  the  saae 
in  intensity  -t  but  opposite  in  direction,  although  this  would  be 
exceptional. 


Elern.  of  turv. 


Page  5 


(53)  CORRECTION  FOK  LGC-vL  *.!&:«£  2 103 

J-f  the  forward  and  th<=  bacic  bearing  check,  that  is,  if  they 
differ  by  180°,  it  is  reasonable  to  assune  that  there  ie  no  local 
attraction  at  either  end  of  the  line.   It  cannot  be  assumed,  how- 
ever, that,  if  they  do  not  check,  the  local  attraction  is  at  either 
or  both  ends;  this  must  be  determined  by  taking  bearings  on  other 
lines  connecting  with  the  two  points.   For  example  a  closed  tra- 
verse may  be  taken  to  illustrate  a  method  of  adjusting  the  local 
attraction.  The  following  set  cf  obeerved  bearings,  given  ooth  in 
sketch  and  tabulated  form,  will  mc.ke  this  plain:- 


/ 

v 
B 

•/ellx 

\ 

/ 

N  &&* 

^ 

\ 

v 

L/n^  if.Jet.'M'r'?     if 
j 

r:   ~IT  "  7;  n 

5.  O^dli'"^-?  !  1  (-r>'fC  '  -'OM 

-^  1  . 

4fcs,^ 

/s 

*v» 

^v< 

^••\        TT 

4  •  G    N  ,f>t»<"4  o  '  ^  j 

oo 

H  58*40  r 

V-~ 
s^\0, 

^-V 

3-/i               ': 

i-tv'^oV    ^  50  ' 

S38*40'W 

^c* 

*\ 

\  / 

x 

3-CJS»°5tt£:; 

4-ao' 

S3O°)0'e 

d*& 

T&0\   <•• 

X 

r 

C-5|                       1 

4^/ic:5o'w    -PC-' 

N  30"  W'^' 

^ 

^^V^ 

*"     •"/ 
J     ^ 

c-^1     :';  -£°/5'.Yi 
l                    j 

-30' 

56/c45'5V 

£\     /N 

\        .x 

A5>>  ^ 
%£ 

or             if 

X-I°45E          00 

W^C45"£ 

\/^ 

D  ^ 

"^t^I^J^i 

:    oo  1 

/V35V/V 

A-DI            h 

S  ^C")°'X.!  F~            HO 

-''-—            *-—  .                     W".  • 

S35°^'£ 

i-  -  -  ...     . 
1.           , 

' 

1 

in. 


Elem.    of  Surv.    1A 


/.ssf.gnrrent  6 


Page  6 


At  A  and  D  it  may  be  assumed,   Bjjaoe  th«  forward  and  back 
bearings  check,  that  there  is  no  local  attraction]  hence  A  -  B  IB 
probably  correct,   N  58°  40'  E;   and  B  -  A  should  be  adjusted  to 
read  S  58°  40'  W;   likewise  D  -  C  is  probably  correct,  N  61°  45'  E; 
hence  C  -  D  should  be  adjusted  to  S  61°  45'   W. 

Evidently  there  is  then  local  attraction  from  a  source  af- 
fecting the  needle   at  both  B  and  C.     Here  the  forward  and  back   Dear- 
ings   (B-C,  C-B)   differ  by  40',   and  one  half  of  this  amount  added  td 
29*  50'   and  also  subtracted  from  30°  50'  will  bring  the   bearings 
into  agreement.    Thus  for  this  ease  the   adjustments  are  made.      The 
data  is  tabulated  as  shown  above,      The   interior  angles  may  now  be 
computed  and  will  be  found  to  check,   as  they  should  (nearly)   in 
practice. 


54)   COMPUTATION   OF   IMKRIOR  «MGIEi  FRO,.:  BEARINGS 

By  referring  to  the  adjoining  figure,    the    bearings   being 
the.  adjusted  values   in  the   traverse   just  cited;,  it   is  easily  ob- 
served that   the  -?.ng.U   ,-BC   is  the  sum  of  the    baok  bearing  B-A  and 


BC 


D 


."  '• 


El  em.    of  Surv. 


Page  7 


the  forward  bearing  B-C.      ^ence    -d-A&C  =  &8°40'  •*•  50°10!  =  88°50'. 
Likewise,   angle  D  is  the   sum  of  the  back  bearing  D-C  and   the   for- 
ward bearing  D-A.     tience    £CDA  =  61°45'   +  35°00'  =  96°45'.      The 
angle  BAD  is  found  by  adding  the  forward  bearing  of   .-,-B  to  the 
back  bearing  of  A-B  and  subtracting  this  sum  from  180°.        180°  - 
(58°40f   -*•  35°00')   =  86°   201.      Also /BCD  =  180°   -   (61°45'   +  30C10J) 
-   88°  05'. 

Many  rules  are  given  by  the  various  authors  of  texts  on 
surveying,    but  by  far  the  best  and  the  simplest  method  is  as  follows: 

Sketch  the  meridian  (magnetic  or  true;    in  accordance  with 
the  bearing)   and  determine  the  desired  angle  by  geometric  addition. 
A  further  illustration  using  general  values  for  angles  and  bearings 
here   follows : 


0 


0  = 


L  — 


MtIV 


Pi  L  - 


o  ihe   e^L 

If  -f  io  n , 


Elem.  of  Surv.  1A        Assijnw^nt  6  Page  8 

Check:  The  sum  of  the  inter j.cr  angles  of  any  polygon  is  equal  to 

twice  as  many  righ+  angles  as  the  figure  has  sidse,  J.BSS  four 

right  angles.   The  figure  hare  has  five  sides,  Twice  5  -  10, 

from  which  subtract  4,  giving  a  remainder  6   Therefore,  a  five 

sided  figure  gives  6  right  angles  or  540°.   In  general  S  =  (2n  -  4)  90°. 

This  formula  is  also  \7titten   S  -  (n-2)l83c. 

(55)  TRAVERSING  BY  DEFLECTION  ANGLES 

Traversing  by  deflection  anglss  is  somstim^s  a  convenient 
method,  the  angles  both  exterior  and  interior  being  easily  calcu- 
lated.  If  the  deflection  angles  are  measured  around  a  field  con- 
secutively in  either  direction  (either  all  right  of  ail  left  de- 
flection) these  angles  constitute  the  exterior  angler  of  the  poly- 
gon; their  sum  for  any  polygon  is  360°.   'i'he  interior  angle  at 
any  vertex  is  190°  minus  the  exterior  angle  at  that  vertex}  the 
sum  of  all  the  interior  angles  is  180°  times  the  number  of  side? 
minus  360°,  or  in  general  S  =  180n  -  360  =  (2n-4)  90°. 

56)  RANGING  OUT  LINbS 

Ranging  out  is  best  done  by  observing  the  deflect? oa  angle 
and  recording  it  as  right  (R)  or  left  (L)  at  sach  charge  of  bear- 
ing.  This  is  especially  true  for  a  traverse  that  does  not  close, 
as  a  road,  rail-road,  boundary  line,  or  ditch,  the  rangirg  of 
which  consists  of  several  parts  of  straight  lines  or  lines  and 
aurves. 

To  measure  a  deflection  angle,  set  up  the  instrument  at 
the  forward  end  of  a  line  and  back-sight  on  the  other  end.   Then 


Elera.    of  Surv. 


Assignment  6 


placing  the  eye  at  the  opj.oe1t.e  si^ht,   turn  the  Jine   of  sight 
right   or   left   as  the   case  may  be  inrf  re»rt  the    angle   passed  over 
by  the  line  of  sight  when  bisecting  the  next  point  in  order.     As 
follows : 

To  range   cut  the   line  0  A  B  C  D  E  by  deflection  set  the  in 
strument  at  A  and  back- sight  on  0.      ^'hen  turn  fore -sight   on  B   and 

.      L 

A  ^^-3\      13 

"^'^  *  -"'•- p 


read  a°  R.     Next  occupy  B,    and  back-sight  on  A;  turn  lore-sight  on 
C  and  read  b°.     Then  at  C  read  c°  L;  at  D,    d°   L.      The    aigle  A  is  ' 
180°  -   a°.      3    is   ISO0  -  b°,    etc. 

Ahe  direction  of   lines,    or  their  bearings  are   often  given 
in  azimuth.      Ihe  azimuth  of  a  line  is  its  bearing  measured  in  de- 
grees in  clockwise  direction  from  either  the  north  or  south  point 
of  the  horizon;   either  the  magnetic  or  the  true  north  (or   south) 
may   be  chosen  as  zero  azimuth.      This  method  will  be  more  fully  ex- 
plained  later,   under  transit   surveying. 


REFERENCES : 

Iracy,   pp.    378  -   383 

Breed  &  Hosmer,   pp.    29  -  30,   Vol.    I. 

Johnson,    pp.    34  -  38. 

Raymond,    pp.    83  -  85. 


.•    •••.?••  ..     ,; 


.  ..T   .;,  •  :.- •  •        •.;.-..<  ..        •  •  •     ;      ,         •    -'  -          •    • 

•  '    ,  •  •    ••  •       ',.  •  !  ',•,'•'-.  .    •         •        '  '       •     •  "  '      •    •'•        •          ,"•'<••'  .••-•'.- 


:      •     '        . .          .  *;        -.•'...•;       , 


'••  '      .'  I    • 


El em.    of   ^urv.    IA 


PROBLEMS 


c5  rnu.ent   6 


P&ge    10 


1.  The  courses  ana    bearings   of  a  certain  traverse   are  at  follows: 
A-B,    S  35?   52'   3:   3-C.   N  ?1°34!   E;      C-l,   K    18°26'   fc;      D-E,   due 
West;     E-A,    S  41°09!  W.      Find  the  interior  angles  and  the   error 
of  closure,     toake  a   sketch  of  the  field. 

2.  A  triangular  field  was  surveyed  with  compass   and  the  deflection 
angles  v-ere  taker,  as  fellows:     at  A-B.,   93°15';  B-C,    150°30'; 

C-A,    116°11'.     Compute  the   interior  angles,  and  give  the  discrepancy. 
Sketch  the   field. 

3.  A  certain  survey  recorded  magnetic  bearings  as  follows:      1-2, 

K  43°15'   E;   2-3,    S  73°18'   E;      3-4,    S  83'23'   W;      4-1,   N   80°17'   E. 
if  the  magnetic  declination  at  the  time  was   12°15'   E,  what  was 
the  true  bearing  of  each  line? 


OF  CALIFORNIA  EXTENSION   DIVISION 
Corresoondence     Courses 
Surveying-lA  Elements   of  Purveying  Swafford 

Assignment  7 
THE  LE\EL  AID   I'i'S  USE 

FOREWORD  : 

This  assignment  will  deal  v;ith  the  level,  one  of  the  most 
important  instruments  used  by  the  surveyor.  Many  of  the  principles 
treated  in  this  part  of  the  course  are  fundamental.  You  are  urged 
to  master  the  subject  of  leveling,  not  omitting  the  slightest  de- 
tail, because  much  that  follows  in  the  subject  of  surveying  depends 
upon  the  material  given  here. 

THE  LEVEL 

In  its  usual  form,  the  level  is  an  instrument  for  determining 
the  heights  (elevations)  of  points,  lines,  and  surfaces  from  some 
known  surface.   It  consists  of  a  spirit  level  and  a  telescope,  so 
combined  and  adjusted  as  to  enable  us  to  determine  elevations. 

The  illustration,  Plate  I,  shows  a  plain  type  of  surveyor's 
level,  which  will  be  fully  explained  in  a  subsequent  paragraph  in 
this  lecture.  For  the  present  let  as  turn  attention  to  a  few 
definitions  of  fundamental  impcrtence. 

level  surface  is  one  that  is  everywhere  perpendicular  to 
:he  plumb-line  drawn  to  a  point  on  that  surface.   Such  a  surface 
is  not  a  plane,  but  is  curved  in  all  directions.  As  it  will  ap- 
proach very  nearly  a  spherical  surface,  for  the  present  purpose 
will  speak  of  it  as  such. 


Elem.  cf  Surr.  IA        Assignment  7  Page  2 

The  surface  of  a  body  of  water  at  rest  is  level;  and  a 
large  body  of  water,  such  as  a  lake  or  ocean,  is  known  to  be  curved. 
In  the  more  exact  work  of  leveling,  the  surveyor  actually  measures 
and  determines  the  curvature;  in  the  less  exact  work  he  determines 
only  a  tangent  plane  or  several  tangent  planes  which  suffice  for  '. 
the  purpose  in  hand. 

A  level  line  is  any  element  of  the  level  (curved)  surface. 
A  plane  can  have  only  straight  lines  lying  in  its  surface,  a  plane 
tangent  to  a  le\el  surface  meets  that  surface  in  only  one  point, 
the  intersection  of  the  plumo-line  at  that  point.  Hence  a  straight 
liue  and  a  level  line  coincide  only  in  that  point  (called  point  of 
tangency)  where  a  line  drawn  directly  to  the  earth's  center  meets 
both  lines. 

The  points  along  any  vertical  line  may  have  surfaces  passed 
through  them  and  thus  a  vast  number  of  concentric  spherical  surfaces 
may  be  found.   These  surfaces  are  designated  by  the  heights  of  a 
point  in  each  above  (or  below)  a  certain  agreed  surface  called 
Datum  or  datum  level. 

Datum  ie  generally  taken  to  be  mean  sea  level,  although 
any  other  surface  may  be  assumed  for  reference.   Points,  lines, 
or  surfaces  referred  to  the  datum  surface  are  said  to  be  so  much 
above  (or  below)  datum,  the  distance  being  given  in  the  usual 
linear  unite.   Since  it  is  not  alwayst  practicable  to  use  mean  sea 
Ie ve 1  as  datum,  other  reference  planes  or  surfaces  nay  be  selected. 
For  .Tioet  purposes  these  are  just  as  good;  but  where  the  established 


Eleni.    of  £urv.    1A  Assignment  7  Page   3 

levels  are  to  be   of  a  permanent   and  extensive  character,    see-level 
is  the  best  reference  plane  and  should  be  studiously  sought. 

[i)  IHT.  SPIRIT  I£VBL 

The   spirit   level  is  a  simple  instrument  consisting  of  a 
ightly  sealed  glass  tube,   or  phial,  almost  filled  with  liquid, 
ter,   alcohol,    or  ether,    imprisoning  a  small  quantity  of  air  in 
the  part  not  filled  with  liquid.      This  air  constitutes  the    bubble 
s  it   is  called,  on  which  observation  is  made  in  the  use  of  the 
pirit  level.      The  tube  with  its  contents  of  liquid  and  air  is 
enerally  briefly  called   "oubole  tube".      The  bubble -tube  it 
lightly  carved,    so  that  when  placed   longitudinally  in  a  horizontal 
oeture,   the  convex  surface   is  uppermost.      'Ihus  the  bubble  of  en- 
losed  air  ie  forced  by  the  many  times  heavier   liquid  to  the   summit 
f  this  curve,  and   thus  caused  to  occupy   a  fixed  position  for  a 
iven  horizontal  one   of  the  containing  tube.      Just  ae  the  plumb-bob 
nd  its  cord  enable  one  to  determine  a  vertical   line,    so  the  bubble- 
ube  may  determine  for  us  a  horizontal  or   level  line;  and  by  the 
ombined  use  of  plumb-lrne  and  Dubble-tube,  aiany  desiraole  quen- 
ities  may  be  measured,    lines   located,    and  relations  estaolished. 
he  spirit   level  enters  int,c  the  construction  of  many  useful  in- 
truiaents  and  in  its  use   aecones  ths  surveyor's  constant  reliance 
'or  determining  horizontality  and  perpendicularity.      inhe  compass, 
escribed   in  Assiga-nent  5,   usually  carries  two  bubble-tubes.     The 
pirit   level  is  an  essential  part  of  the    engineer's   level,   the  sur- 
yor's  or  engineer's  transit,   and  the   plane-table  alidade.      It  is 


Elem.    of  Surv.    lA  Assignment   7  page  4 

also  used  for   leveling  tapes,  for  plumbing  rods,   etc. 

The  spirit-level  is   sometimes  made  in  a  circular  form  that 
is  very  convenient  for   some  purposes;  for  example,   for.  leveling 
the  ple.ne-table  and  for  plumbing  rods.      The  upper,  curving  surf  ace 
of  the  circular  level,  aads  of  glass,    is  a  portion  of  a   spherical 
surface,  the  sphere   being  of  great    radius  as  compared  with  the 
size   of  the   level.      The   imprisoned  air,  which  is  the  bubble   in 
this  form  as   in  the  tube  form,  rises  to  the  highest  part  of  the 
glass  cover,   and  so  the  bubble   is  made  to  occupy  the  center  of  the 
circle  when  the  plane   of  the  level  is  horizontal.      This  accomplishes 
all  that  can  ordinarily  be  accomplished  by  means  of  tiso  bubble- 
tubes  placed  at  right  angles  to  each  other;  a  level  plane  may  be 
determined  by  the   single  circular  level,  which  is  often  of  great 
advantage. 

IE)  PRINCIPLES  OF  THE   ENGINEER'S   ILVEL' 

1.  If  a  horizontal  line  be  made  to  rotate  about  a  point  in 
itself,   but   always  maintainxng  a  horizontal  position,    it  will 

generate  a  horizontal  plsne. 

•     • 

2.  Straight   lines   lying  in  this  plane  will  be  horizontal   lines. 

3.  All    lines  passing  through  the  point  about  which  the  given 
line  rotates  will  be  perpendicular,  to  a  plumb-line  at  that  point. 

In  the  engineer   s   level  the  rotating  line  is  the    line  of 
:ollimation  of  a  telescope  which  may  be  prolonged  as  the   line  c£ 

• 

si^ht     to  an  indefinite  distance. 

Ihis  line  of  collimation  is  made  perpendicular  to  a  plumb- 
line,  called  the  vertical  axis  of  the  instrument,  about  which  the 
telescope  rotates,  therefore,  in  a  horizontal  plane. 


Elsm.  of  ourv.  lA 


Assignment  7 


Pege  5 


Conceive  then  this   line  determined  by  the   telescope's  axis 
sweeping  out  a  horizontal  plane  tangent  to  the    true   (spherical) 
level  surface  at  the   point  of  intersection  with  that  surface  of  a 
plurao-line,   the  vertical  axis   of  the  instrument,      fhe  height  of 
this  plane  aeasured  along  the  plumb-line   (vertical  axis)   from  some 
assumed  plane  of  reference   (datura  plane)    is  called  the  height  of 
instrument  (K.    I.  ) 


Figure  14 

In  the  illustration  (Fig.    14}   L. T.    is  a.  level  telescope   sup- 
ported upon  a  tripod  that   is   in  adjustment,   carefully  set,    and 
"leveled  up"  %-ith  the   tripod  legs  firaly  planted  in  well  chosen 

isitione   in  the  midst  of  e  numoer  of  points  at  the  surface  of  the 
ground,   a,   o,   c,   c,   e,   f,  and  also  &n   estao lished  point  B.lt. 
(bench  marie)   shovn  to  the  left.      The  telescope  rotated  about  ite 

vertical  axis  will    determine  the  horizontal  plane  A  B  C  D  E  F  G. 
If  now  MS  measure  ti.e  heights   oi   the  horizontal  plane  above  the 

points   on  the  ground  we  obtain  the  quantities  aA,    bB,   cC,  dD,   eE, 
JET  »nd  (B.h- )  G.      Now  the  height   of  B.k.    above  the  plane  of  refer- 
ence, called  datum  level,    is  known,     riold  a   rod  on  B.fcL.   and  direct 
the   line   oi    sight  toward  it   and  read  the  distance   (B.M. )fi.        Add 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 

CORRESPONDENCE  COURSES  IN  ENGINEERING  SUBJECTS 

PLANE  SUBVEYING 

COURSE  X-lA 


PLATE  I 

16-iNCH  DUMPY  LEVEL 
Length  of  telescope,  16";  diameter  of  objective,  1%";  magnifying  power,  28x;  total  weight,  25  Ibs. 


PLATE  II 

PRECISION  ENGINEERS  '  Y-LEVEL 
Length  of  telescope,  18";  diameter  of  objective,  1%";  magnifying  power,  33x;  total  weight,  27%  Ibs. 


Elem.   of     Surv.    1A  Assignment  7  Page  6 

this  reading  of  the  rod  to  the  height  of  B.M.  which  will  give  tne 
height  of  the  level  plane  above  datum.  This  is  called  the  height 
cf  instrument,  H.I.  The  plane  iiJCDLF  is  at  the  height  H.I.  above 
Datum. 

To  find  the   height  of  a,   b,   c,    etc.    above  datum,   hold  a  rod 
(level-rod;   at  a,   fa,   c,  etc.    and  direct  the   line  of  sight  to  it 
and  read  the  heights  cA,   b3,  cC,    etc.      subtract  these  r  eadings 
from  H.I.    and  the  differences  will  be  the  elevations  of  the  points 
on  the  ground  above  Datum. 

Note  well  that  the  rod-reading  on  3.M.    giving  the  quantity 
(B.M. )G  is  added  to  the  height  of  B.M.   to  give  the  H.I.,    and  that 
the  rod-readings  aA,    b3,   cC,   etc.    are  subtracted  from  H.I.  to  give 
the  elevation  of  the  points  on  the  ground,      hence,    since  the  Sp- 
reading is  added,  we  regard  it  always  as  a  -f  quantity,  called  a 
plus  sight,    and,    fcr  e.   like  reeson,  the  point  whose  elevation  is 
to  be  ceterminea  we  regard  as  a   -  quantity,    called   a  minus   sight. 

The  terms  B^clc-sight  for   plus  sight  and  Fore-si^ht  for  minus 
sight  are  also  commonly  ussd.     You  should  get  the   foregoing  con- 
ceptions clearly   in  ;nind,   as  uuch  confusion  is  often  occasioned  'by 
a  vague  understanding  of  these  very   simple  matters. 

The  following  is  B   orief  description  of  the   engineer's 
level.     For   simplicity   the  Ijarapy  level   is  chosen.      The   student 
should  procure  a  descriptive  catalogue  or  manual  cf  surveying  in- 
struments  such  as  is  published  and  for  sale  at  small   cost  by  the 


Elem.    of  Surv.    1A  Assignment   7  Page  7 

leading  instrument  makers  -  L.C.    Berber  &  Sons,    Huff  and  Buff, 
W.   &  L.   E.   Gurley,    riausch  &  Lomb,    Ihe  A-    Lietz  Co.,   and  others. 
The  manuals  go  much  beyond  the  text-book  on  the  subject, 'and 
usually  give  a  deal  of  information,  tables,   and  material  of  great 
value  to  student  and  engineer  alike.      The  best  way  to  know  the  in- 
struments is   by   intelligent  handling  of  them  guided  by  a  skilled 
instrument  man  or  by  following  directions  given  in  good  text-booke 
or  the  manuals  najied  above. 

TH1  DUMPY  il/vEL 

Ae  shown  in  the  illustration,  Plate  I.,  the   Dumpy  Level  con- 
sists of  a  horizontal  bar    fixed  to  a  vertical  axis  which  turns  freely 
in   a  well  made  socket,      io  the  bar  a  telescope  and  a  spirit  level 
are   firmly  attached.      Ihe  whole    is   supported  upon  a  tripod  and  a 
leveling  hsad.      The   latter   is  used  to  set  the    bubble  in  a  central 
position  in  its  tuoe,   thus   Cringing  the   line  of  coliimation  of  the 
telescope   (which  should  be  parallel  to  the  .axis  of  the  bubble  tube) 
into  a  horizontal  position.      ihe  line  of  coliimation  can  then  be 
made  to  sweep  out  a  horizontal  plane  by  turning  it  upon  the  vertical 
axis   of  the  instrument,  prolonged  indefinitely  in  the    line  of  sight. 

The  telescope  contains  two  optical  ports,  the    ooject-glass 
at  the   larger  end  and  the   eye  piece  at  the  smaller  end  of  the  tele- 
esope  tube,      i'he  object-glass  is  a  douole-convex  lens  usually  of 
the  compound  variety  to  overcome  the  tendency  to  color  dispersion 
of  light  by  unequal    refraction,   called  chromatic  aberration.      This 
lens   is  s  Iso  shaped  in  &  manner  to  reduce  as  far  as  possible  a 


Elem.  of  Surv.  IA        Assignment  7 

distortion  known  as  spherical  aben:ati_on.     Both  of  these  faults  of 
simple   lenses,  would  be  very  trouolesorae,   if  the   skill  of  the   in- 
strument maker  could  not  combine  and  construct   lenses  so  as  prac- 
tically to  eliminate  aberration.      For  a  full  explanation  of 
these  matters  you  should  consult  a  reliable  work  or.  optics;   in 
general,   a  good  high-school  text  on  physics  will  be   sufficient. 

When  the  light  from  the  various  parts  of   sny  object  to 
tvbich  the    large  end  of  the  telescope   is  directed  passes  through 

the  double-convex  lens,    it    is  made  to  converge  within  the  tube  in 
such  a  way  as  to  form  a  real  but  diminutive  image   of  the  object 

sighted.      This  real  iiaage   is  inverted.      If  now,    the  real  image  be 
viewed   by  another  lens,  the  eye-piece,    it  will  be  magnified  so 
that    its  details  will  be  more  distinct   aid  it  -Brill  appear  nearer 
and  also  larger.      In  some   instruments  a  compound   eye-piece   is  em- 
ployed, which  re-inverts  the   image  that  was  inverted  by  the  object- 
glass;  thus  the  thing  viewed  through  the  telescope  appears   in  its 
normal  position  or  erect.      On  this  account  a  telescope  with  the 
compound  eye-piece  is  called  an  erecting  instrument.      The  sort 

having  a  simple    (single)    iene  for  eye-piece  is  an  inverting  instrument. 
The  inverting  type  is  preferable     for  many  optical  reasons; 

and  when  once  tne   engineer   oecoraee  accustomed  by   long  use  to  the 
inverted  itua^es,   he  may  prefer  an  inverting  to  an  erecting  instru- 
ment.     The   inverted  image   is  brighter,   and  more   snarply  defined, 
and   it   gives  a  flatter  field,  all  of  which  are  very  desirable. 
However,    it  is  not    intended   to  disparage  the   erecting  eye-piece,  as 


Elem.  of  Surv.  1A        Alignment  7  Page  9 

all  makers  construct  excellent  instruments  cf  this  latter  kind,  snd 
many  engineers-  prefer  to  use  them.  Within  the  limits  of  ordinary 
surveying  the  erecting  instrument  is  quite  adequate  and  very  con- 
venient. 


^^  ,     _J_J___J_   --..-,  -    .._  .,_        T,. 
-_.-^r«. . . — ~^r  "•"""      ~' 


Of-  ll  12  V 

Section  of  Erecting  Telescope 

Figure  15 
The  accompanying  cut   shows  a  section  of  the  telescope.  '  0 

is  the  objective   lens   and   1,    I-,',    1_,   lg  ere  a  comoination  of  lenses 
constituting  the  eye-piece.      The   lenses  are  named  in  order,!,  the 
object   lens;    1.,   the  amplifier;   lp,  the  field  lens;    1*  the  eye-lens. 
Together  they  form  a  compound  magnifier   (microscope)   which  enlarges 
end  re-inverts  the   real  image  formed  by  the   objective-lens,   0. 
This  real  image  falls  at  C,   at  which  is  placed  a  ring-like  diaphragm 
carrying  two  fine  threads,   either  of  platinum  or  spider  web,  called 

oroes-hairs   or  cross-wires.      Thus  the    image  viewed  through  the  tele- 
Esope  has  the  image  of  the  cross-hairs  lying  distinctly  upon  it 

The   line   joining  the  intersection  of  the  cross-hairs  and  the  op- 
tical-center of  the    objective-lens  with  the  optical-axis   of  the 
telescope,  vriien  in  coincidence   form  the    ''Line  cf  Collimation"  to 
reference  has  several  times  been  made. 


(61)   THE 

Another  common  form  of  engineer's  level  is  the  vllye   Level 
shewn  in  Plate  II,   in  which  the   horizontal  bar,    instead  of  having 


El era.    of  3ur7.    IA  Assignment  7  Page   10 


the  telescope  attached  to  it,   carries  at  each  end  &  clutch  for 
holding  the  telescope  called  a  %e   (or  Y)    since  it  resembles  the 
letter  Y. 


The  wyes   are  accurately  ground  to  shape  on  their  supporting 
surfaces  in  ivhich   rest  two  collars  forming  a  fixed  part  of  the 
telescops-tube,     The  collars  also   are  very   accurately  ground  to 
cylindrical   shape  and  of  equal  diameter,    so  that,  when  resting  in 
the   supporting  surfaces  of  the  wyes,    the   optical  axis   of  the 
telescope   (the   line   of  collimation)   is  perpendicular  to  the  ver- 
tical axis  in  whichever  of  its  two  postures   it  may   lie.     Thus  the 
telescope  may  be  turned  end  for  end  in  the  wyes,    or   rotated  about 
its   axial   line  when  resting  in  it.     Each  wye  has  fitted  to  it  a 
cover-clip  that  fastens  down  either  with  a  pin  or  other  device. 
In  one  collar  (usually  the   eye-end )   is  a  notch  into  which  a  pin 
on  the  clip  fits,  thus  holding  the  tube  firmly  and  preventing  its 
rotating  when  the  clip  and  pin   are  down. 

The  bubole-tube   in  the   v;ye-level  is  fastened   by  short  col- 
umn-like supports  to  the  telescope-tube   so  that   it   may  be  adjusted 
to  be  parallel  to  and  lie   in  the  same  plane    (i.e.   truly  parallel) 
with  the   line   of  coliimation  of   the  telescope.      See  Assignment  XIII 
on  Adjustment  of  Instruments. 

The  wye-level  has   lor.g  been  in  favor  with  engineers  on  ac- 
count of  the  readiness  with  which  certain  instrumental  adjustments 
oaj    be  made,   and  perhaps  on  account  of  the  belief  that   it  embodies 
some  features  thought  to  be  indispensable  in  an  instrument   of 
presicion.      Tnese  features  are,   however,   rather  more  fanciful  and 


Elem.    of   Surv.    lA  Assignment  7  Page   11 

traditional  than  real  or  even  convenient.      The  dumpy-level  is 
coming  more   and  more  in  favor  every  day;  and  for  precise   leveling 
other  and  unquestionably  better  forms  have  superseded  the  wye- 
level.      Still  the  -rye  is  by  no  means  an  obsolete  pattern,   and  is 
etill  preferred  by  many  surveyors.      You  are,  therefore,   particularly 
advised  to  acquaint  yourself  with  the  structure,    adjustment,  and 
use  of  this  instrument. 

(62)   THE  HAED-iEVLL 

The  hand-level  is  a   simple  and  very  useful  leveling  tool. 

It  is  specially  adapted  to  reconnaissance   and  preliminary  work,    or 
to  levels  Tfhere  a  low  degree   of  accuracy  is  permissible. 

The  Locke  hand-level  is  the  simplest  and  most  commonly 
used  type,   but  others  of  a  more  refined  and  elaborate  construction 
are  also  made  by  most  manufacturers  of  instruments.      They  are  der 
scribed  in  catalogues   and  manuals.     The  Aoney  hand-level  and  clin- 
ometer,   and  the  Atwood  combined  hand-level,   clinometer,    and  com- 
pass  (a  really  universal  instrument)   are  the  principal  rei'ined 
forms  of  this  useful  little  tool. 

The  very  elaborate  preciss-levels,    such  as  are  employed  in 
the  Ccast  and  Geodetic  Surveys  and  other  extensive  leveling  work, 
are  not   in  general  use    by  engineers  ~nd  will  not   be  described  in 
the  present  course.      The  manuals  referred  to  furnish  illustrations 
anc!  descriptions  for  those  who  desire  to  know  more  about  them. 

The   level   in  any  of  its  forms  is  used  to  determine  heights 


. 


Elen.    of  Surv. 


Assignment  7 


Page   12 


or  elevations  from  an  assumed  datura,    to  measure  differences  of 
elevations  or  altitude,  to  run  profiles,    lay   off  cross-sections 
for  fill  and  excavation,    locate  contours,   etc.,    etc.     the  work 
of  such  nature"  will  be  explained  and  amplified  in  subsequent 
assignments.  Trill ch  will  deal   specifically  v/ith  each  class   of 
problems  - 


1.  What  do  you  understand  by  H.I-? 

2.  Explain  3.  S.  ,  F-S.  ,  B.fci. 

3.  Why  is  a  level   line  not  a  straight   line? 

4.  A  level  set  up  on  the  shore  of  a  lake  had  its   line  of  sight 

in  a  plane  6.5  feet   aoove  the  water  in  the    lake.     The 
readings  taken  on  a  rod  held  at   various  points  gave   at 
A  4.  3  ft.,     .     at  B   8.7  ft.,   at  C  6.5  ft.;  how  do  the 
heights  of  these  points  compare  %vith  the   level  of  the 
water   in  the   lake? 


References  : 


Tracy,  Chapters  XIX  and  XX. 
Raymond,  Ch-    III. 

Johnson,   pp.    55  -   56,   60  -  64. 
Breed  &  Hosraer,   pp.    72  -  78,  Vol.    I. 


UMVLhbHY  Oi'  CALIFORNIA  EXXLwSIUlM   DIVISION 
Correspondence      Courses 

Surveying-lA  Elements   of  Surveying  Stafford 

Assignment  8 

LEVELING  PROiiLLwS 

FOREWORD  : 

fhis   aid  the   following  assignment  will  describe  the  use   of 
trie  engineer's   level   (A)   for  determining  Difference   in  Elevation; 
(B)   for   Profile   Leveling;    (C)    for   Estaolishing  3ench  Maries;    (D)    for 
Cross-section  Leveling;    (E)    for    Leveling  for    (1)   Excavation   (tiorrovv- 
pits)   and   (2)   Fills;   and   (F)   for  Finding  trades  and  Contours.      The 
methods  of  making  notes  foj   the    various  problems  here  treated  will 
also  be    shown. 


f'63)   3EKLRAL 

The   level   should  always   be   set  up  on  firm  ground  at    a  con- 
venient   station  for    observing  as  many  points  and  as    large  a  range 
as  is  consistent  with  good  work  within  the   limits  of  accuracy 
sought.      It   is   rarely   necessary  to  set  the   level    over   a  point,    the 
elevation  of  which   is  desired,    or   immediately  upon  a  line   joining 
two  points   to  be  measured.      Indeed,    such  a  setting  will   often  frus- 
trate the  purpose   in  hand   cr  greatly  interfere  with  accuracy  in 
observation,   as  will  be  perceived  if  you  recur  to  the   conception 
of  a  horizontal   plane  at    elevation  H.  I. 

(64)  BENCH  MARKS 

If  elevations   of  points   are  desired  above  any  agreed  plane 
of  reference   (or  datum  level;,    a  bench  mark  (B.M.  )   of  known  elevation 
must   begin   or  dote   the  work. 


Eleivi.    of   Surv.    1A  Assignment   3  Page   2 

Should  the  extent   of  the    leveling  require  that  the   level    be 
moved  from  place  to  place,   points   of  firm  and  often  of  durable  na- 
ture must  be  selected  or  improvised  on  which  an   observation  (fore- 
sight) may  be  made  at  one   setting  end  another   observation  (back  - 
sight)   may  be  made  at  the  following  setting.      These  are  called 
Turning  Points,   perhaps  because  the  measurements  are  made  from  a 
new  horizontal  plane  svept  out   by  the  line   of  sight  at  each  setting. 
(65)  Turning  points  are  usually  selected  or  established  as   the 

•work  of  leveling  pro  eeds,  cfld  much  depends  upon  their  kind,  i'hey 
should  always  be  sufficiently  firm  to  support  the  rod  held  upon 
them  while  ooth  0  fore-sight  and  a  back-sight  can.  be  taKen  upon 
them.  They  should  be  situated  in  open  spaces  where  both  sights 
may  be  clearly  taker,  free  from  obstruction,  not  too  near  or  yet 
too  remote  from  the  instrument.  The  distances  from  two  successive 

turning  points  (T.P's)   to  tue    instrument   should  be  about  equal. 
This   last  requirement  is  for  the   purpose  of  eliminating  any  error 

in  the   parallelism  of  the   axis  cf  the   bubble-tube  with  the  line   of 
coll inat ion  of  the  telescope.      For,    if  the  vertical    axis   be  truly 
vertical,   but  the    lint    of  sight  for   any   reason  oe  not   perpendicular 
to  it,   then,  when  the   bubble   is   at  mid-point  of   its  tube  for   each 
sighting  on  two  points  equidistant  from  the   instrument,   these  two 
points  will  be   in  the  sane    level  plane.      The  line   of  sight   in  such 
case    "sweeps   out"  the   surface   of  a   cone  end  the   vertical   axis  of 
the   instrument   is  also  the  axis  of  this  cone.     The  position  of  the 
cone    is  either  erect,    stand in§  upon  its   oase,    if  the   line   ol    sight 
is   inclined  downward,    or   inverted,    standing   upon   its  apex,    if  the 


.    of   Surv,    1A  Assignment   8 

line   of  sight   is   inclined  upward.     Movv,    since  the  two  points  are 
at  equal  distances  from  the  instrument   (i.e.   from  the  vertex  of 
the  cone)    and  the  axis  of  the  ccne  is  vertical,    a  horizontal  plane 
perpendicular  to  the  vertical  ajcis  may   be  made  to  pass  through 
both  points,      hence  they  are  at   the  same  elevation  and  a   line 
joining  them  is  a   level  line. 

(66)   TEE   IEVEL  ROD 

For  the  purpose  of  making  vertical  measurement  a  rod  is  used, 
on  which  is  merged  off  a  scale  of  linear  measure,  feet  and  inches, 
or  oetter,  feet  and  decimals  of  feet,  or  in  other  cases,  meters  and 
fractions  of  meters. 

The  common  form  is  in  two  parts,  each  about  7  1/2  feet  long, 
1  1/2  inches  wide,  3/4  inches  thick,  graduated  upward  upon  the  front 
side  and  continuing  downivard  on  the  reverse  side  of  each  part.  The 
parts  are  fitted  together  and  are  held  in  place  oy  two  bronze  sleeves, 
The  upper  sleeve,  turned  toward  the  back,  has  a  vernier  acale  on 
its  edge,  by  which  the  least  interval  capable  of  being  measured 
mey  be  determined.   The  upper  sleeve  also  carries  a  clamp  sere./, 
with  a  large  milled  head,  by  means  of  which  the  rod,  when  extended, 
may  be  held  firmly  in  position.   Thus  the  rod  raay  be  used  either 
short  (up  to  7  feet)  or  lon^  (to  about  13  1/2  feet  when  fully  ex- 
tended).  The  lower  end  of  the  rod  is  fitted  with  &.  metallic  shoe. 

(e?)  A  TARGET 

The  target,  made  of  .aetal  in  circular  or  other  convenient 
shape,  about  5  inches  in  diameter,  has  an  oblong  opening  in  its 


.  .     :  . 


:       .: 


•:]  .  : .. 


; 


.     . 


Elem.    of  Surv.    IA  Assignment  8  page  4 

middle  part.      It  is  suitably  fitted  to  slide  up  and  down  upon  the 
front   section  of  the  rod.      On  one  edge  of  the  opening  a  second  ver- 
nier  is  attached  for   reading  the    least  measures   as  with  the   first 
vernier.      The  face   of  the   target   is   divided   into   four  equal  quad- 
rants inrhich  are  colored  alternately  white  and  red,  their  horizontal 
line  of  division     being  coincident  with  the    zero  of  the  vernier 
scale.      A  clamp-screw  similar  to  the  one  mentioned  above  is  carried 
by  the   target,   by  means  of  which  the  target  may    tie   set  at  any   point 
along  the   front  section  of  the  red.      It  may  also  be  fixed   at  the 
7  foot  mark  of  the  rod  on  a  segment  of  the  front   section  that   is 
firmly  glued  and  screwed  upon  the  rear  section.      The  best  rods  are 
made  of  well   seasoned,   straight-grained  maple  wood,   neatly  fashioned 
ano   highly  finished,    and  the  divisions  are  accurately  and  distinctly 
narked  in  black  and  red  upon  a  white  ground. 

(08)   I'flE  VERNIERS 

The  above  mentioned  verniers  are  constructed  ae  follows: 
For  a  direct-reading  vernier,   a  space  equal  to  9  of  the   smallest 
divisions  on  the  rod  is  divided  into  10  equal  parts  on  the  vernier. 
Let  us  take  the  common  graduation  in  feet,   tenths  of  feet,    and 
(the   least  division  on  such  s  rod)   hundredths  of  feet,      i'hen  in 
the   vernier   for   this   graduation  (Direct  type)  will   consist   of  9/100 
feet  divided   into  10  equal  parts,    end  each  vernier   interval  will 
be   9/1000  feet.      If  now  the  horizontal   line   of  the   target,   which 
coincides  with  the   zero  or   lowest   line   of  the  vernier  divisions, 
be    e*i  at  any  point   or.  the   rod,    say  at  4  ft.  ,   3  tenths,   and   6  hun- 
dredths  and   some   fraction  above  the   6   hundredths  mark,   the  vernier 


'.  .'    :j 


1  .'          *         v 

' 


•  '.  I 


Elera.    of  Surv.    IA  Assignment  S  Page  5 

will  determine  for   us  the  number  of  thousandths   oeyond  the  6  hun- 
dredths  mark.      For    example,  with  the    setting  of  target  as  given 
above,   4.36+  ft.,   count  the  vernier  divisions  beyond  the  6  marie 
to  that  vernier  division  which  coincides  vrith  a  hundreqth  division 
Une   of  the   ro£.      This  will  give  the   number   of  thousandths   of  a 

foot  to  be  appended  to  the  reading  aoove.      For  instance,    if  the   . 

full 
numoer  be  ?  vernier  divisions, the  exact/., rod-reading  will  be  4.367 

any 
ft.      And   so  f or < other  cases. 

In  reading  a  direct  vernier  always  count  along  forward   in 
the  direction  of  the  main  rod  sc*le   and  add  this  count  to  the 
reading  upon  the  rod  as   shown  by  the   last  full   division.      This  will 
be  upward  on  the   front   section  of  the  rod,    and  downward  on  the  re- 
verse  side   of  the  rod  when  using  the  rod  extended. 

Generally,    and   for  good  reasons,    a  better   form  of  vernier, 
called  the  Retrograde  Vernier,   is  now  employed,      i'his  is  constructed 
by  talcing  a  space  equal  to  eleven  least  rod  divisions  and  subdividing, 
it   into  10  equal  parts.      Thus  one  division  of  the   vernier    is  (on  the 
retrograde  vernier;    11/10  of  one  hundredth  of  a   foot,      to  if  the 
zero  of  the    vernier   scale    fall  at  a  point   oeyona  a  full  hundredth 
division  on  the  rod-scale  ana  the  vernier  scale   be  applied   in  a 
reverse   (retrograde,;    direction  to  tht   scale   divisions  on  the   rod, 

the  count  on  the  vernier   scale   backward  to  the  line  of  coincidence 
will  measure  the  number  of  thousandths  of  a  foot   oeyond  the   last 
i'ull  hundredth  rae.rk.      ^ence   re-^c   tue   i'ront   of  the   rod  upvard     es 
always,    but    read  the   retrograde  vernier    downward) likewise  on  the 


Elem.    of  Surv.    IA  Assignment  8 

reverse   scale   for    long  rod,   read  the  rod  divisions  downward  and 
count  on  the  vernier  scale  upward.      The   following  illustration    ' 
shows  settings  for   both  direct  and  retrograde  verniers  for    both 
short-rod  and  long-rod  readings.      You  are  advised  strongly  to 
make  many  similar   settings  and   record  the   readings  for   a  rod  to 
which  you  may  have  access.      Check  back  the  readings  recorded,    Dy 
resetting  the  target  for  each  of  the  whole   series  of  observations. 


~  *l  -.O  i~-  -«  »?   J-  N-;   v  -    o 

i 
4  —  LJJLJ_LL          » 

r*- 

r     '  1       '        -I        '        !       \ 

v_>*                          *o                          *-          < 

\ 

/    /<?tjrf>   /£ 

(69)   USL  OF  THE    LEVLL  hOD 

When  taking  readings   on  a  target  rod,    be  sure  to  close  the 
rod   down  to   its   shortest,   length   for   short-rod,    or   set   the    target 
exactly  on  the  highest  mark  for    long-rod..      Also  be  careful  that 
nothing     such  as  mud,   gravel,    or   other  foreign  matter  intrudes 
itself  between  the    shoe  and  the    point  (B.M. ,   T.P. ,   or  other  sur- 
face)  the  height  of  which  ic   sought.     This  could  cause  an  error 
of  several  thousandths   or  even  hundredtns   of  feet,    thus  voiding 
the   accuracy   of  the  measurements.      A  proper   beiich  mark  is  usually- 
free  from  foreign  natter   or  can   easily  be  rendered  so.      fuming 
points   should   be   selected  upon  a   stone  firmly    imbedded   in  the 
ground,   the   root   of  a  tree,    or  &   stump  or  post,    a  curb-stone, 


Elem.  of  Surv.  1A 


Assignment  3 


Page   7 


doorsill,    etc.  ;   T.P. 's   may   also  be   put   down  in  the   fora  of  wooden 
stakes  or  metal  pins  driven  well  into  the  ground.     A  good  form  of 
T.P.    is  easily  made  of  a  triangular  piece   of  light  plate  iron, 
which  has    a  round  head  rivet  set   in  its  center  and  the   corners 
turned  dov»n  sharply   at  righx  angles  to  the   plate,  as   snown  in  the 
figure. 

When  such  a  turning  point    is  pressed 
down  into  the  -eatth,    especially    in  light, 
marshy,    or  sandy  soil,   the  rod  can   be  held 
upon  the  rivet  head  at  the  center,   thus  in- 
suring an  excellent  support.      If  a  hole    is 
punched  in  the  plate  so  that  a  cord  or  chain 


ft  9. 1 7 


may  be'  attached,    it  can  easily  be   lifted  up  and  carried  from  point 
to  point,      be  careful  also  that  the  T.P.    is  even  and  horizontal, 
for    if  not,  the   rod  might  be  too  high  in  one  position,  and  too 
low   in  another. 

(70)   THL  USE   OF   THE  TARGE I 

In   leveling,   the  use  of  the   target  greatly  facilitates  the 
work  of  accurate  sighting  and  at   long  ranges,   several  hundred  feet 
distant,    it    is  nearly   if  not  quite   ind  ispensaDle   to  good  work. 
Several  forms  of  targets  are   in  use,   but  the  circular  with  quad- 
rantal  divisions   is  perhaps  the   best.      The  angular  target  which 
is   in  reality   tv/o  half  ellipses   viewed  at  an   angle    of  45  degrees 
and  thus  appearing  as   a  circular  disk,    is  ouch  in  favor  with  many 
engineers.      J»uch  a  target  presents   a  sharply  defined  vertical   edge 


Elen.    of  Surv.    1A  Assignment   3 

(the    intersection  of  the  tivo  semi-ellipses) ,  which  assists  the 
instrument  man  in  determining  whether  or  not  the  red   is   in  the 
X'ertical  plane  through  hie   station;  and  the  straightness  of  two 
horizontal   lines,    continuous  as  one    line,   enables  him  to  know 
that  the   rod   is  also  in  the  vertical  plane  at  right  angles  to 
the  first  plane,    or,   in  other  words,   plumb.      For,    if  the   rod  be 
in  the  first  vertical  plane   the  vertical  cross-hair  will  coincide 
with  the   intersection,   and   if  not    in  the  second  vertical  plane, 
the  horizontal  divisional  lines  will  forr.  either  a  wide  vee   C^") 
when  the  rod  leans  toward  the    instrument,    or  will  form  a  wide 
inverted  vee   (^\)    when  it  leans   bacicward,   as  shown  Oy  the  hori- 
zontal cross-hair- 

(71)   PLUtiB  ROD,   HUD   IEVLLS 

It  is  very   important'  in  level  work  that  the   rod  be  held 
plumb  when  a  reading  is  taken,  as  any  deviation  from  perpendicu- 
larity to  the    level  surface  will  give  a  false  height,  and  the  true 
height   is  the  thing  sought. 

Rod   Levels  are   frequently  used,   especially   in  nice  v;ork. 
These  are  either  two  small  spirit-level  tubes  encased  in  a  bronze 
block  that   fits  squarely  upon  a  corner  of  the  rod,    or  a    single 
level  set   in  ?.  block  that  may  DC  applied  by  the  rod-man  when  re- 
quired. 

The  circular  or   bulleeye   level  is  also  used  for  this  jjur- 
pose.      It  is   supported  upon  the   rod  by  a  bracket  that   secures  the 
true  position.      A  plumb-boo  and   line  ma-    also  De  used.      The  rod -man 


I  * 


Elen.  of  Surv.  1A          Assignment  8  Page  9 

can  also  often  secure  the  rod1 8  verticality  by  aligning  the  same 
by  eye  with  convenient  structures  near  at  hand  or  in  the  not  too 
remote  distance. 

Still  another  way  is  to  place  the  rod  in  the  vertical  plane 
through  the  instrument  as  nearly  as  possible,  which  is  the  less 
difficult  feat  of  the  two;  then  at  a  signal  from  the  instrument 
man  to  'Hvave  rod",  he  may  slowly  tilt  the  rod  forward  and  backward 
while  the  man  at  instrument  determines  by  trial  the  highest  po- 
sition of  the  horizontal  line  of  the  target.   This  last  is  th« 
least  satisfactory  method,  but  in  the  absence  of  other,  better 
means,  it  should  not  be  neglected. 

(72)  CHOOSING  SETTINGS  AND  T.  P.'e. 

In  moving  from  setting  to  setting  of  the  level,  or  in  se- 
lecting turning  points,  it  is  essential  that  ooth  rod-man  and  in- 
strument man  use  careful  judgment  in  each  case.  Often,  after 
much  trouble  in  choosing  such  positions,  they  are  found  unsfetis- 
factory  from  the  fact  that  the  level  is  either  too  high  or  too 
low.   This  is  especially  liable  to  De  the  case  on  very  uneven 
ground  or  in  regions  where  rocks  and  trees  or  brush  render  sight 
difficult  or  impossible.   At  times  the  levelers  must  "hasten 
slowly",  or  at  lenst  exercise  much  ingenuity  and  good  judgment. 
Often  the  longest  rod  is  not  long  enough  or  the  level  plane  at 
H.  I.  cuts  the  ground  below  the  foot  of  the  rod.  Nothing  can  then 
be  done  but  either  to  set  up  the  instrument  anew  or  to  select  a 
more  suitable  turning  point,  if  it  is  this  that  makes  the  difficulty. 


, 


El  era.  of  Surv.  IA          Assignment  8  Page  10 

By  roughly  sighting  along  the  barrel  of  the  telescope  when  approxi- 
mately adjusted  to  level,  an  advantageous  setting  may  often  be 
quickly  determined. 

It  has  been  the  purpose  of  the  author  to  give  detailed 
directions,  as  the  student  of  this  course  is  supposed  to  do  all 
instrument  and  field  work  unassisted  by  sn  instructor  to  direct 
his  operations.  Much  must  always  remain  vague  until  by  experience 
in  handling  instruments  and  laying  out  woric  in  the  field,  indis- 
tinct, misunderstood,  or  erroneous  mental  images  (such  as  one  may 
acquire  from  bocks  of  description  and  illustration)  are  cleared 
up  and  corrected  by  actual  practice.   Therefore,  it  is  v.rith  earnest 
sincerity  that  you  are  again  urged  to  delve  into  texts  and  manuals 
on  surveying  in  order  that  you  may  secure  an  intimate  acquaintance 
with  both  instruments  and  surveying  methods.   The  references  at 
the  end  of  each  chapter  to  standard  works  will  be  of  much  value  to 
those  who  have  access  to  and  will  properly  use  such  books. 

(73)  GENERAL  PROBLEM.  IN  LEVELING.      A  -  Difference  in  Elevation 

The  problem  is  to  determine  the  difference  in  elevation 
between  two  points  A  and  B. 

Set  up  the  level  at  any  convenient  place  about  equidistant 
from  the  two  points  to  be  ooeerved  and  follow  directions,  ooserving 
the  cautions  given  in  the  preceding  part  of  this  lecture.  Level 
the  instrument,  reversing  over  each  diagonally  opposite  pair  of 
foot  screws,   the  rod-man  must  now  hold  the  rod  upon  the  point  A 
in  a  vertical  position  with  target  out  of  range  of  line  of  sight 


•        ! 


I       .      . 


'  :,  ' 


v 


Elem.    of  Surv.    IA  Assignment   3  Page   11 

so  that  the   instrument  :nan  may  read  through  the    teleecope  the 
approximate  height  of  tne   horizontal  plane.      Then  call   to   or  signal 
this  number   vr°£-reading)   to  the  red --man,   ?rho  will   quickly  set  the 
target  as  directed,   but  hold  it   if  within  comfortable  reach,  and 
rr.ovc    it  up  or  down  until  signalled  to  clamp  it.     At  the   signal 
"wave  rod",   he  will  tilt   it  forward  and  oaclcward.     Determine 
whether  the  target   is   r.t  the  highest  point;  that  is,  whether   the 
line   of  sight   ie   never   below  the  horizontal   line   of  the   middle   of 
the  target   <\rsd  -vhether    it  cuts  this   line-  but  once  at  each  forward 
or  backward  rucveirent    of  the   rod  when  it   is    "waved".      This  is  the 
correct  target  setting,  which  the   rodiaan  nov^  reads  fcr  himself, 
F.nc,    ir.  psssing  the:    instrument  tc  occupy  the  point  B,  the  instru- 
ment man  also  reode  the   setting  and   records  it  in  hie  field  book: 
when  it   ie   found  to  igree  -.vith  the    reading  determined  Dy  the    rod- 
rr.an-     fce  calls    "checs"   if  correct;   otherwise  the  rod  should  again 
be  held  upon  the  point  and  re-read  to   insure  aosolute  agreement. 
At  point  b   the  sa.-ae  process   is  repeated  and  the   elevation  of  B 
taken  -  that   is,   the    rod  in  ooth  cases  has  measured  the  distances 
frorc  the   points  A  and  B   to  the  level-plane   sv«ept  out   by  the   line 
of   sight,    or  vhat    is   the    sz.xe  thing,    the  distance   of  the    two  points 
below  this   letel-plane.       ihe   difference    jetveen  the  two  rod  readings 
is  the   difference   in  elevation   sought.      If  the    two  points  A  and  B 
are  very  distant  fr?m  each  othtr,    cr   if  the  intervening  ground   is 
very  sloping,    or   if  the  t\/o  points  can  not  both  be   observed  from  a 
convenient   setting  of  the   instrument,    it   bsco/aes  necessary  to  select 
one  or  more  turning  points  and  to  observe  on  these,   finally  closing 
or.  the   second  given  point. 


• 


Flem.    of  Surv.    1A 


Assignment   8 


Page   12 


To  illustrate  this   and  tc  furnish  a  correct  form  of  notes, 
tsuce  the   following:     First   setting    (1)   Rod-reading  on  A  4.376  ft.; 
(2)    roc-reading  on  T.P.,,   6.843  ft.;    reaove   level  to  second  setting; 
(3;    rod-reading  on  T.P.p   3.572  ft.;   (4;   rod-reading  on  T.P.p,   5.831  ft.; 
third  getting  of  instrument;    (5)   rod-reading  on  T.P.g,   2.7-*3  ft.; 
(6)   rod-reading  on  T.P.,,   6.745  ft. ;  fourth  setting;    (7)   jcd-reading 
on  i.P.    ,    (on  the    long-rod,    i.e.,   rod   extended  with  the  target 

O 

clamped  at  the  topmost  graduation;  note  that  this  reading  is  made 
on  the  back  part  of  the  red    and  downward) ,   9.357  ft.;    (8)   rod-reading 
on  8,   3.852  ft.,  which  completes  the  course  from  A  to  B   through 
three  T.P's.     We  now  proceed  to  tabulate  these  in  notebook  form  as 

follows  : 


p/  f  f  e  re  i  >  +  ic(    L&^e  Is 


0 


Z 


M43 


5-35T 


foicjkT  cn    jjc.fc. 


T  P,  on  firm  fml»<&f*<t  UK  £ 


.«3'  I 


5^52,.. 
33.27> 


in 


/^.  //>  r/*^  /^^3 

b  is    i 


42^3fi/: 


A- 


The   illustration  is   intended  to   show  t\vo  pages   of  Field    IJote-book 
of  approved  form. 

Note:-   It   is   best,   when  the   difference    in  elevation   should   be 
measured  with  precision  that   a  series  of  return  levels   be  run 


Elem.    of  Surv.    1A  Assignment  3  Page   13 

beginning  upon  B   and  closing  upon  A.      A'he   T.P's.    of  the   return 
levels   should  be  ehosen  at  any   set   of  points  other   than  those 
used  in  working  from  A  to  3.      Thus  a  new  set  of  determinations   is 
made  which   should    "check"   closely,   within   aoout  0.005  of  a  foot 
of  the   first  determination, 

(74)   GEHERAL  PROBLEM  IN   LEVELING  B   -   Profile  Leveling 

This  problem  will  undertake  to  get  the  elevation  of   a  series 
of  points,  called  stations  along  a   line  A  either    straight  or  crooked; 
so    as  to  chart  the  profile. 

Assume  a   line  staked  off  by  tape  or   chain  measures  giving 
stations  along  the    line  at   regular  intervals  of   100  ft.,    50  ft., 
or    any  other  desired  number  of  feet  and  levels  taken  at  these   and 
intermediate    stations.      A  line,    as   shown  below,    is  the  horizontal 

4-»tf>       4r56__ 

U 

1  2.     .  '•  " 

projection  along  which  a  profile  is  desired.   £he  line  A  B  C  D  is 
laid  off  in  stations  0  (at  A);  0+50;  1;  1+20  (at  B);  2  (which  is 
also  used  as  a  turning  point);  2+50;  3  (at  C; ;  3+50;  4,;  and  4+75 
(at  D).   L-^  and  Lg  are  positions  at  which  the  level  is  set  up,  the 
same  being  about  equidistant  from  B.M.  (a  bench  mark  at  known  or 
assumed  elevation)  and  from  which  rod-readings  can  conveniently 
be  taken  at  each  full  or  intermediate  station.  With  level  set  at 
L.  and  carefully  leveled  up,  read  the  rod  at  B.M. (+sight; ;  then 
rod-readings  at  0,  0+50,  1,  1+20,  Z  will  be  -  sight  readings. 


;     .  /• 

!.•'•'       ,    •    ' 


Elem,  of  i_urv.  1A 


Assignment  8 


Page  14 


The  instrument  is  then  set  up  at  L, ,  carefully  leveled  as  before, 
and  a  +  sight  taken  upon  2  as  a  turning  point.  After  this  read 
the  rod  held  &t  2+50,  3,  3*60,  4,  -i+50,  and  4+75.  hecord  in  note- 
book  ae  follows: 


-' 

8.5 

:    //I    ;     Fj>. 

i 

0,. 

t 

» 

i 

•Mtt 

'  '*-  j^rS*  , 

I 

I 

1   D-  /^-     fat  .(JQO  &•     &bo\/€    OcTilrft). 

0 

;     ISO. 

Of  50 

EE 

119. 

..—. 

Uu 

i  f  A/y 

^ 

. 
• 

!  1     I-  V,1 

|4.-^-$ 

119. 

009 

h-  50 

, 
j 

17?. 

~" 

2-5-00 

8  «5S 

•*j 

179 

ISO 

TTP^MM^    S^d^    «•    7-^ 

^t5o 

l 

i 

n$. 

^s 

mci-Jfcet    3^0-  2^/70  TFT 

i 

765 

3i~o 

J7.53C 

IftO. 

"" 

r^«.«r^j^  *•  4t*«*»<Mj 

K'O 

j 

k^ 

I8£. 

723 

.    j 

6~f  a  ttcH'T 

[~ 

tea 

_  .... 

T^to"/"  pH)filt  -/6   huhJt+el'jkj 

1 

'.4*7.$ 

~"   "•  —  ' 

.  _i*f^ 

IB3. 

Smf5  f/^cA--  /06/5!   ^ 

-707  ; 


ley 

t 

X 

I    /                 "r  rr    ret  1  1  (  n 

\-t.Snt,  • 

/a 

IS  i    4^ 

to  5o&[          i 
i 

182 

I                     ! 

'    ! 

1              ! 

I 

• 

2(9. 


Elen.    of  Surv.    1A  Assignment   3  Page    15 

To  find  the  e lex  at ion  of  H.I.   above  datum,   add  the  rod- 
reading  on  3.M.   to  height  of  B.M-    above  datum,   end  record  under 
E.I.    in.  the  table.      -   181.00  +  4.752  gives   185.758.      Subtract  the 
st-.tion  rod-readings   (which   ?.re  all   foresights;    from  h- 1-    to  find 
their  elevation  and    record  under  elevation.      This  is  done  for  each 
full   station  (or  intermediate  station)  until  the  T.P.    is  reached. 
Here  -we  add  the    back-si^ht  on  the  T.P.   to   the  elevation  of  I. P. 
obtained  from  the  previous  fore-sight   and'. thus  find  the  H.I.   for 

the   second  setting   of  the    instrument.     Fran  this  point  on,  the 
rod-readings  are   again  ail   fore-sighte,  which  ere  mw  suotracted 
from  the  nev/  K.I.   tc  find  the  elevations  of  the   remaining  stations. 

A  careful   study    ol    the  notes  and  the    accompanying  profile 
chart  will  give  a  clear  notion  of  the  meanings  of  the  various 
quantities   and   of  the  graphical   means   of  illustrating  them. 

The   scales  used  in  charting  are  usually  chosen  ?n.th  a  view 
to  the   purpose   of  the  work:-  here  to  show  the   rise  and   fall   of  a 
rond  arade  line,      i'hs   horizontal  scale  is   rather   suiall  but  for  the 
purpose  are  ply   ie.rge  to  give  necess*  r,,    details;  while  the  vertical 
scale  is  comparatively   large,   cr  exaggerated  to  diovr  elevations   in 
greater  relief.      This  is  c-istomar^  although  the   relative   scale 
values  are  usually   of  much  lower   r*.tio. 

Other   leveling  problems  will  be  taken  up   in  Assignments 
XIII   and  XIV. 


Elem.    of   iurv.    IA  Assignment  S  Page   16 

PROBIEMS 

1.    fhe  following  set  of  level  notes  taken  for  finding  the   dif- 
ference  in  elevation  between  B.M-  ]_  and  B.M.  2  give  the  tabulated 
data.     Find  the  difference   of   elevation. 

Sta.          3.S.          H.I.  F.S.  Diff. 


B.M.I 

8.78 

T.P.  l 

6.81 

4.83 

X.  P.  2 

2.74 

7.68 

I.  P.  3 

11.41 

5.82 

X.P-4 

0.75 

9.74 

B.M.  o 

6.81 

B 

2.   Fron  the 

following  tabulated 

field  notes  find  the  elevations 

of  all   stat  ions 

on  the   line;  sketch 

the  profile. 

Sta. 

D.  8«          H.  !• 

F.S.            Dili.   El             Elev. 

E.M-7 

6.22 

126.75 

0  +  00 

6.03 

0  +  25 

6.45 

+  75 

7.14 

1  +  00 

6.10 

-*•  50 

5.16 

2  +  00 

6.01 

+  25 

6.50 

+  50 

6.83 

+  75 

7.04 

T.P.I 

7.34 

5.63 

3  +  50 

6.45 

+  75 

7.16 

4  +  00 

8.17 

+  25 

8.49 

+  50 

7.83 

+  75 

7.20 

5  +  00 

6.85 

References : 


Tracy,   Chap.   XX.1 

Raymond,   pp.    50   -  SO 

Johneon,    pp.    71   -  78 

Breed  &  Hosraer,  Vol.    I,   pp.    232  -  2V7 


«.,   . 


• 


Uni  iV^j  o  ii  "i    Or     '...^.".r  o:  :-,  1'.  L..j._:.  oi  .<:,    ^ITvAalOti 
Correspondence      Courses 

Surveying-!;!  tleruents  of  purveying  Stafford 

Assignment    9 

THE;   TRANSIT   AND   ITS   USES 

FGREV.OhT  : 

The  purpose  of  this  assignment  is  to  describe  at  length  the 
Xrf.nsib,  and  to  acquaint  the  student  as  far  as  possible  vith  the 
vide  range  of  its  uses  in  surveying.   Problems  of  a  general  char- 
acter requiring-  the  transit  in  their  solution  will  be  de?.lt  with 
in  a  subsequent  assignment. 

(75)  THE  TRANSIT 

The  transit,   a  truly   universal    instrument  for  surveying  and 
engineering  work,    is  for  the  work  of   surveying   in  all  its  branches 
by  far  the   best  and  ncet  adaptable.      In  a  complete  engineer's 
transit,    such  as  that    illustrated  in  Plate   III,   are  combined  the 
compass,   the    levsl,    the  theodolite,    and  the   techyraeter.      It   is  used 
to  measure  angles   in  both  a  horizontal   snd  a  -vertical  plane;   to 
determine  heights  and    distances,   magnetic  or  true   oearings,  and 
angles  in  azimuth  and  altitude.      In  its  most  refined  forms,   it  is 
capable   of  the  nicest   or  aiany   desired  determinations   of   sucn  quan- 
tities  as  are  named  above.      It  enables  the  engineer  to  accomplish 
his  -work  with  great   precision  and   satisfaction,      with    the   aid   of 
suitable  attachments  the   transit   is  capable  of  solving  ir^an^    oi   the 
intricate  problems   confronting  the   engineer   in  the  realm  oi   astronomy. 


UNIVERSITY  OP  CALIFORNIA  EXTENSION  DIVISION 

CORRESPONDENCE  COURSES  IN  ENGINEERING  SUBJECTS 

PLANE  SURVEYING 

COURSE  X-lA 


PLATE  IV 
MOUNTAIN  AND  MINING  TRANSIT 

Fitted  with  4-inch  full  vertical  circle  graduati 
solid  silver,  vernier  reading  to  minutes,  alumi 
protection  guard,  and  full  extension  tripod. 


PLATE  in 
COMPLETE  ENGINEERS'  TRANSIT 

Fitted  with  5-inch  vertical  circle,  provided  with  a  double  vernier, 
reading  to  minutes. 


Elesi.    of   Surv.    IA  Assignment  9  Page  2 

(76)  TRANSIT  DESCRIBED 

A  transit  comprises  primarily   a  telescope  similar  in  con- 
struction to  that  described  under  the  LEVEL.      The  telescope   is 
mounted  upon  a  plate   bearing  two  standards  in  v/hich  it  turns  com- 
pletely around  on  trunnions   in  a  vertical  plane   and  the  plate,   stand- 
ards, snd  consequently  the   telescope,   may   also   be  moved  about  a  ver- 
tical axis   in  a  horizontal   plane.      This  part,  then,  called  the  ali- 
de.de,  hes  two  degrees  cf  freedom  of  motion,   i.e.    it  may  be  turned 
in  azinuth  and   in   Altitude 

(77)  THE.  FLATZS 

Th-r   plates  of  the  transit  are  really  three,    but   generally 
only  two  are  spoken  of.      i'he  plate  to  which  the   standards  are  at- 
tached,  the  alidade  plate,    rests  upon  a  second  plate  with  v/hich 
the  first  is  concentric.      A  vertical   axis  may  move   about  through 
their  centers  together   or   independently   on  carefully  constructed 
spindles.      These  spindles  fit  one  within  the  other  and  both  into 
a  suitable    socket  bored  into  a  third  plate  which  forms  the   base  of 
the   instrument.      The  third  plate,    sometimes  called  the  foot-plate, 
IE   securely  attached  to  the  supporting  tripod  end  forms  virtually 
the  tripod -head. 

The   alidade-plate  turns  on  its  spind" j  over  the   lover  plate; 
the   lov.er  plate  turns   about   its   spindle   over  the   foot-plate.        The 
foot-plate   is  securely  fixed,   usually  upon  a  tripod  that   stands  on 
the  earth.      Again  the   alicade-plate  carries   one,    and  generally  two 
circular-arc  verniers.      The   lower  plata  is  graduated  in  degrees 
and  fractions,    by  which  angles   in  the   horizontal  plane  may  be 


Elerc.    of   Surv.    lA  Assignment  9  Page  3 

rueisurfcd.      faese  verniers  wnich  are  needed  to  measure  small  frac- 
tions of  angles  v,ill  be   fullj   described   later  on. 

(76)   CLHi/>P-bCRLttS,   I-nFGLKT-SChEYvo 

AS   stated  aoove  the   nlidade-p.la.te   and  the   graduated-plate, 
the  outer  graduated  rim  of  Trhich  is  called  the   limb,  may   oe  moved 
together  or  separately    iu  azimuth.      In  order  that  this  :aay  oe   ac- 
complished,  each  pifcte  has  a  clamp-screw  oy  which  the  upper  may  oe 
secured  to  the    lower  or  the    lower  to  the  foot-plate.      When  in  this 
clamped  position  i*v   it.    deei;rabie  to  rotate  either  plate  through  a 
sinall   en&le,   for  careful  &ud  nice  adjustments,    each  plate  is  fur- 
nished with  r  t?ngent-  screw  to  accomplish  this   object.      They    are 
called  tangent  -scrfevvs,    because  they   act  along  a   tangent  to  what 
may  be  assumed  to  be  the  plate's   circumference.      The  location  and 
the  form  oi   eacb   of  the   p.bo^e  e  crews  are   such   as  to  enable-  the 
instrument  nian  to  find  a  particular  one   at  pleasure,      jjn  exaini- 
nation   of   a  transit   or   oi    the  detailed   illustration,    Plete  V,  will 
reveal  them  to  you. 


(79)    I.EV 

AT^tsched  to  the    foot-plate,    iu  which  the    spi.idlos   are  fittea 
and    in  which  thej-   turn,    ars  four   (or   in  some   instruments   only  three  ; 
lugs   extending  radially,    intc  which  fit   smooch,  well-cut  screws, 
having   large  milled  heads,   one   in  each  lug.      These  screws,  called 
foot-screv,s,   rest   upon  the   fixed  tripod  head  and  permit  the   spindles 
to   be   shifted  until   they   are    or  ought   into  a  vertical  position. 
Since  the  two  plates  are   fixed  at   right  angler,    each  to  its  own 


Eien.    of   Surv.    IA  Assignment   9  Page   4 

spindle,    oy  adjusting  the    sp:.ndies  until   they  are  vertical,   the 
plates   are  raaae  horizontal  at  the   same  time. 


(so)  cu'jMP  AKD  TANGENT  SCREV,  OL  TELESCOPE 

Attached  to  the  right  hand  standard  are  the  clamp  to  lock 
the  horizontal    axis  at  the    trunnion,   and  the  tangent  screw  to  give 
it  gradual  motion  through  a  small  angle   in  the  vertical  plane   of 
the   telescope.      The  three  tangent  screws  aow  described   bear   against 
opposing  springs  thet  hole  the  moving  part  firmly,   except  vfaen 
pushed  forward  or  withdrawn  backward  by  the  screw. 

(81)  LEVELS  UPON  iL-IL 

The  alidade-plate   has  two   small    spirit-levels  attached  at 
right  angles  to  each   ether   oy  adjustable  screv/s,  which  enaole  the 
levels  to  be   orought   into  parallelism  with  the  plate,    i.e.    at 
right  angles  to  the   vertical  axic  through  the   spindles.      In  some 
transits,    one   of  these    levels    is  attached    to  the   left   hand  st-?ndard 
th^xt   supports  the   telescope,    but   its  office    is  the   same  as   if  it 
•werelying  upon  the  plate. 

(82)  COMPASS  ^HD-  JisAGK&TIC  NELDLL 

Commonly  a  transit  has  P    compass  plate  ann  a  magnetic  needle 
fixed  to  the  alidade-plate,   by  which  magnetic   bearings  may  be  taken, 
and  magnetic   declinations  may  be  determined.      The  magnetic  needle- 
is  of  especial  value   in  checking  angles  measured  upon  the  graduaied 
or  lower  plate  of  the   instrument. 

(33)    LEVEL  ON  TELESCOH, 

A  spirit-level,    several   inches   in   length,   and  usually   of 


..'.'.         1 ..,.'.     . 

. ...  . 


UNIVERSITY   OF    CALIFORNIA    EXTENSION   DIVISION 
CORRESPONDENCE   COURSES   IN    ENGINEERING   SUBJECTS 

PLANE  SURVEYING 

COURSE  X-lA 


UJftlW 

SSW*y*ltfer  trf* Ml 


PLATE  V 
Cross-section  of  a  Transit. 


CORRECTION 

No.  29  should  read  "Shade  Holder"  instead  of  "Vernier  Glass  Fr 
No.  30  should  read  "Vernier  Glass  Frame"  instead  of  "Shade  Holder." 


Eleza.    of  Surv-    Lu  Assignment   9  Page   5 

great  sensitiveness,    is  connected  parallel  to  the  telescope   by 
mear.s   of  short  columns.     By  *  use   of  this   level  the   line  of  sight 
may  be  r.ade  horizontal   ae  in  the    engineer's   leveling  instruments 
already  descrioeo.      This   enables  the  engineer  tc  fix  the  horizontal 
plane   for  the  usual  purposes  of   leveling,   or  for   securing  angles 
of  elevation  or  depression,  etc. 

(84)   VERTIGO,  CIRCLE   OR  VERTICAL  /JRC 

Attached  to  the  horizontal  axle  of  the  teleecope   (with  com- 
plete transit)    is  a  graduated  circle  or  a  graduated  arc,  with  ac- 
companying verniers,  for  measuring  vertical  angles   (angles  of 
elevation  or  of   depression). 

(95)    OTHER   ACCESSORIES 

A  variation  arc   is  soraeti.nes  connected  with  the  compass- 
plate.      J-t   is  often  of  great  convenience   in  setting  off  the  dec- 
lination. 

A  gradienter   screw   is   in   some  transits   substituted  for  the 
usual  tangent-screw  to  the  horizontal  axis.     Uy  this   small  angles 
in  elevation  (or   depression)  may   be  set  or  determined  independent 
of  the   vertical  arc.      It   is    a  screw  of   very   refined  make,   the 
thread  of  which  ano  the  divisions  on  its  head  being  EO   graduated 
as  to  secure  an  elevation  of  one  foot  at  a  distance  of  100  feet 
or  200  feet  for   one  full  turn  of  the  screw. 

(66)    IRE  GRADUATION   OF  THE   LOWER  PLATE 

The  lo^'er  plat©  is  graduated  in  degrees   and  fractions  of 
degrees,   usually  to  halves  or  thirds;   i.e.,  the  smallest  division 


UNIVERSITY   OF   CALIFORNIA    EXTENSION   DIVISION 
CORRESPONDENCE    COURSES    IN    ENGINEERING    SUBJECTS 

PLANE  SURVEYING 

COURSE  X-U 


METHODS  OF  GRADUATING  SURVEYING  INSTRUMENTS  AND  POPULAR  STYLES  OF 

VERNIERS  FURNISHED 


A 

FIG.  21 
Double  vernier  reading  to  30".     Circle  graduated  to  20'. 


V 

Fi<;.  22 
Double  vernier  reading  to  20".    Circle  graduated  to  15'. 


10 


0 


FIG.  23 
vernier  reading  to  10".     Circle  graduated  to  10'   with  one  row  of  figures. 


Bleu,  of  ourv.  1A          Assignment  9  Page  6 

on  the  graduated  Hub  IE  50  minutes  or  20  minutes  of  arc.   In  some 
instrunents  the  division  is  carried  to  10  minutes  of  arc  but  this 
is  rather  exceptional,  being  too  small  for  ease  in  reading,  and 
of  no  especial  advantage. 

X'he  divisions  are  grouped  in  spaces  oi  b  and  10  degrees 
marked  on  the  scale  by  lines  somewhat  longer  tnan  the  usual  division 
lines  and  numbered  at  the  10,  20,  SO,  etc.,  manes.   The  zero  of  the 
scale  is  indicated  by  a  0  or  A  •   rhe  numbering  is  generally  in 
both  directions,  preferably  through  360°;  one  &et  of  numbers 
being  nearer  to  the  inner  p^.rt  of  the  graduated  ring  and  reading 
clockwise;  the  outer  set  reading,  therefore,  counter-clockwise. 
For  convenience  in  reading,  the  characters  are  slanted  in  the  di- 
redtion  of  numbering.   Some  makers  colcr  the  inner  or  clockwise 
set  in  black,  the  outer  or  counter-clockwise  in  red.   These  and 
other  devices  are  intended  to  assist  in  reading  in  the  right 
direction  and  to  prevent  contusion  of  scales. 

(87)  VtHWIERS 

The  vernier  as  adapted  to  reading  linear  scales  (see  Assign- 
ment 8)  has  already  been  explained.   Now  we  turn  to  the  circular 
vernier. 

On  the  level-rod,  verniers  of  two  kinds  are  used,  the  direct- 
reading  vernier  anu  the  retrograde  vernier.  As  the  retrograde  ver- 
nier is  rarely  used  on  transits,  the  direct  type  only  need  be  dis- 
cussed here. 

One  form  cf  vernier  is  constructed  by  taking  29  degrees 


UNIVERSITY   OF    CALIFORNIA    EXTENSION   DIVISION 

CORRESPONDENCE    COURSES   IN    ENGINEERING    SUBJECTS 

PLANE  SURVEYING 

COURSE  X-lA 


METHODS  OF  GRADUATING  SURVEYING  INSTRUMENTS  AND  POPULAR  STYLES  OP 

VERNIERS  FURNISHED 


FIG.  24 
Single  vernier  reading  to  20".     Circle  graduated  to  20'  with  two  rows  of  figures. 


10 


20  '"I        ^rt^'W 

rH^^r 


ao  ilo 

FIG.  25 
Vernier  reading  to  2'.     Circle  graduated  to  single  degree. 


3ft 


A 
FIG.  26 
Double  vernier  reading  to  single  minutes.    Circle  graduated  to  30'. 


Elera.  of  Surv.  1L          .ussigmaent  9  Page  7 

(when  the  smallest  division  on  the  limb  is  the  whole  degree)  and 
subdividing  it  into  30  equal  parts  for  the  vernier  scale.   The 
value  then  of  one  division  on  the  vernier  will  differ  by  1/30  of 
1  degree,  or  2',  from  a  single  division  on  the  limb;  this  value 
ie  called  the  "least  count "  of  the  vernier.   Another  commonly  used 
vernier  is  formed  by  subdividing  2S  half-degrees  (the  smallest 
rivision  on  the  limb  being  a  30*  space)  into  30  equal  parts  on 

the  vernier  scale;  here  we  have  — ** —  =  I1  as  the  least  count. 

29  +  1 

A  vernier  constructed  upon  a  scale  of  20  minute  divisions  in  which 
39  of  these  civisions  are  divided  into  40  parts  on  the  vernier 
would  give  -?.  least  count  of  1/2  minute  or  30";  thus  ii  20'  is  the 

smallest  li.ab  division  and  39  the  vernier  number,  then  — — — 

20'  39  *  l 

vill  equal  •  -  =  1/2'  =  ?0".   The  following  rule  may  now  oe  given: 

R'JLE.   ^Co  find  the  least  count  of  a  vernier  : 

Divide  the  value  of  the  smallest  division  on  the  limb  by 
the  nuraber  of  such  divisions  plus  one  required  in  forming  the  ver- 
nier scale.   In  general,  To  find  the  least  count  of  a  vernier: 

Let  I.e.  =  least  count,  d  =  the  value  in  circular  units  of 
the  smallest  division  on  th*  limb,  n  the  number  of  these  smallest 

divisions  th&t  make  n-f-1  spaces  on  the  vernier-scale;  then 

d 

I.e.  •=.  ~    , 
n  +  1 

unit 
In  this  formula  the   resulting  unit  value  will  be  that^in  which  _d 

is  expressed.     This   of  course  may  then  be  reduced  to  any  required 
unit . 


Elem.    oi'   Surv. 


Fage   8 


Verniers   are  of  two  types,  single    and  double.      The  double 
type  comprises  tv.o  single  verniers  extending  in  opposite  directions 
from  the   initial  point,    or   index,   the  numbering  also  extending,  in 
opposite  ways.      Thus,  with  this  double  vernier,  vrtien  the  alidade 
plo.te  has  moved  over  the  graduated  liiab  clockwise,  the   left-hand 
vernier   is  observed;    out  when  in  counter-clockwise  direction,   the 
right-hand  vernier  is  used,  always  reading,  (for  &  direct  vernier) 
in  the  direction  of  motion.      The  vernier   reading  is  then  appended 
or  added  to  the  reading  on  the  limb. 

For  economy  of  space   another  plan  of  laying  out  the  vernier 
scale   is  sometimes  used.      In  this  style  one   half  of  the   vernier  is 
to  the  right,   the  other  to  the  left  of  the   index  nark.      This   form 
is  called  the    "folding  vernier"  or   "split  vernier"  and   is  shown 
in  Figure   26A-      ]Tb31oTriii£   what  has   already   been  said   respecting 


F o Idir.g  or    "Split"  Vernier 


50 

/•    / 


UlUdl 


I  10 

30 

Figure      26a. 

verniers   in   general,   no  extended  description  of   the   folding  type 
is  needed,      'fhe  net  hod   of  reading  the   folding  vernier   is    as  follows 

Read  the    limb  to  the    last  full  division  passed  over  by  the 
vernier's   index;   then  determine  the  vernier  reading   by  counting 


El em.  of  Surv.  L^.         Assignment  9  Page  9 

along  the  vernier  in  the  direction  of  motion  of  the  alidade-plate 
to  the  line  of  coincidence  as  usual.   If  the  coincidence  does  not 
occur  over  the  first  half  of  the  vernier  scale,  then  continue  the 
count  from  the  opposite  end  of  the  vernier  toward  the  index,  to  the 
line  of  coincidence.  Add  the  vernier  reading  to  the  reading  on 
the  lirr.b. 

Here  the  smallest  division  on  the  limb  is  30';  29  smallest 
intervals  are  divided  into  30  parts  cm  the  vernier;  hence  the 
least  count  of  the  vernier  is  one  minute.   In  the  illustration  the 
movement  of  the  alidade  plate  taken  clockwise  has  brought  the 
vernier  index  past  42°;  reading  the  vernier  forward  to  the  left, 
we  find  no  coincidence  to  the  left  half  and,  therefore,  returning 
to  the  extreme  right  and  again  counting  forward  to  the  left  the 
coincidence  is  found  at  25.   ihis  appended  to  the  limb  reading 
gives  42° £5'  as  the  full,  correct  reading. 

Much  has  been  said  and  several  illustrations  have  been 
given  covering  the  subject  of  verniers.  This  has  been  done  in  an 
endeavor  to  make  clear  to  the  student  this  important  and  well-nigh 
indispensable  adjunct  of  the  engineer's  transit.   The  student  is 
urged  to  acquaint  himself  fully  with  verniers  of  every  variety,  in 
order  that  he  may  be  able  to  read  angles  with  ease  and  dispatch. 
Also  in  using  any  transit  or  other  instrument  on  which  a  vernier 
must  be  read,  be  careful  to  determine  its  "least  count"  first  of 
all. 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 

COBEESPONDENCE  COURSES  IN  ENGINEERING  SUBJECTS 

PLANE  SURVEYING 

COURSE  X-lA 


PLATE  VI 
TRANSIT  THEODOLITE 


PLATE  VII 

MOUNTAIN  AND  MINING  TRANSIT 

FITTED  WITH 
BURT  SOLAR  ATTACHMENT 


lien,  cf  Surv.  lA          Assignment  9  Page  10 

(38)  THE  VARIOUS  UbLS  Of  'IHE  i'RAN£I.C 
A.  Ranging-out  Lines. 

2he  fact  that  the  transit  telescope  can  ba  rotated  in  both 
a  vertical  and  a  horizontal  plane  enables  us  to  make  use  of  it  for 
determining  direction  and  for  prolonging  lines  at  any  angle  desired. 

For  purposes  of  surveying,  lines  must  be  continued  or  pro- 
longed in  certain  desired  positions  upon  the  earth  s  surf ace ,  as 
in  setting  out  a  line  of  division  between  properties,  a  boundary 
line  or  fence  line.   Such  a  line  must  often  be  carried  from 
point  to  point  either  in  &  straight  or  raore  often  in  a  broken  or 
curved  line.  Ranging  out  lines  ie  also  practiced  in  road,  railroad, 
canal,  ditch,  and  other  construction,  and  in  most  problems  in  land 
surveying.   (See  especially  burvey  of  the  Jrublic  Lands,  Assignment 
XIX..) 

Through  homogeneous  media  light  is  propagated  in  straight 
lines;  through  any  such  media,  therefore,  light  emanating  from  any 
distant  source  is  brought  to  the  eye  in  a  path  that  does  not  deviate 
fror,  a  straight  line  unless  its  course  be  interfered  with  or  de- 
flected by  intervening  agency  causing  reflection  or  refraction. 
This  principle  is  the  fundamental  one  in  all  uses  of  the  telescope 
in  surveying  and  in  astrcnor.ical  measurement.  As  mentioned  in  the 
description  of  the  telescope  on  the  engineer's  level,  the  line  of 
coll iraat ion  may  be  prolonged  indefinitely  into  "the  line  of  sight". 
Cbeerve  that  when  the  trrnsit  telescope  is  directed  toward  a  dis- 
tant object,  light  from  thr-t  object  enters  the  large  lens  and  is 


Elera.    of   burv.    1A  Assignment   9  Page   11 

fccu?ed  a^  tne    intersection  of  the  cross-hairs.      In  fact,   a  line 
joining  the  object  viewed  and  the  mid-point   of  the  two  cross-hairs 
is   a  straight  line  traversed  by  a  ray  of  light.     TJe  are  certain 
then  that  we  can  retrace  this   line  of  eight   as  a  straight   line, 
unless  it  is  bent  from  the  straight  course,   by  something  that  de- 
flects  it  -  a  reflector  placed  in  its  path,   or  media  of  rarer  or 
censer  kind  which  changes   its  direction,     iiut  the  purposes  and  the 
practice   of   surveying  are   such  as  to  enable  us  to  eliminate  these 
interferences  or  to  r&ctify   them  with  directness  and  fidelity  to 
the  principle   of   "sighting". 

Ihe    line   of   sight   in  the  transit  telescope  may   be   directed 
up   or   down  by    its   rotstion  upon  the  horizontal  axis   or  t o  right 
or   left   oy  turning  the   plate   and  the  telescope  supports  about  the 
vertical  axis-      Therefore : 
To  prolong   a  straight,   line 

Set  up  the  transit*  at   one  extremity  of  the    line ;   place  a 
marker  at  the  other  end;   fix  the  cross-hairs  upon  the  marker  (in 
coiorron  parlance    "oisect  the  point").      Now  by   shifting  the  telescope 
upward   about   the  horizontal   axis   (i.e.    by  -earning  it  upon  its 
trunnions)    extend  the    line   of  eight   beyond  the  farther  extremity 
of  the  gix'eri  line  and  place  markers  to  fix   it  upon  the  ground. 
Markers,    as  pins  and  stakes,    or  rods  are  commonly   those  described 

under    "measuring  lines  with  chain  or  tape". 

*  To   "set  up  a  tr'nsit"  means  to  place   it   so  that  the  vertical  axis 
points  to  the   zenith  through  a  point   of  occupency   on  the  earth.      In 
that  case  the   plumb-line  attached   to  the   transit  axis  will   be  directly 
in  line  with  the  given  pcint,   vhen  the  plate-bubbles  are  at  center- 
( It   is  assumed  that  the   instrument   is    in  adjustment   as  far   as  the 
vertical    axis  and  plate   levels   are  concerned.)      See  Assignment  XIV 
on  adjustments. 


Elsrn.  of  Surv.  lA          Assignment  9  Page  12 

If  nov;  it  is  desired  to  prolong  the  line  in  the  opposite 
direction,  clamp  the  plates,  adjust  the  line  of  sight  to  bisect 
the  most  distant  point  of  the  line,  in  its  original  length  or  pro- 
longed, and  invert  the  telescope  on  the  trunnions  so  that  the  line 
of  s i£ht  may  be  directed  in  the  opposite  direction;  place  markers 
(pins  or  stakes)  as  before. 

Instead  of  inverting  the  telescope  (called  plunging)  it  may 
be  reversed  in  direction  by  turning,  the  alidaderoiate  through  a 
horizontal  angle  of  380?.   ^his  assumes  that  there  is  no  eccen- 
tricity either  of  the  alidade-plate  or  of  the  vernier  indexes  by 
?/hich  the  angle  of  130°  is  detsrmned,  in  other  words  that  these 
parts  are  in  adjustment.   If  the  plate  adjustnents  are  not  true, 
the  line  will  not  be  straight  but  bent  at  the  point  over  which  the 
instrument  ie  set. 

To  eliminate  such  an  error  use  a  principle  called  double 
sighting. 

(8S)  DOUBLE  SIGHTING 

consists  in  sighting 
Double  eight ing^upoa  one  extremity,  B,  of  a  line  when  the 

transit  occupies  the  other  exiremity  A;  this  brings  the  line  of 
sight  in  a  vertical  plane  through  the  line  joining  the  two  points. 
Turn  the  alidade-plate  through  180*;  sight  thi  telescope  upon  a 
required  point  C,  in  the  reverse  direction;  now  reverse  through 
180°  bisecting  the  first  point  3;  plunge  the  telescope  (i.e.  invert 
it)  and  if  the  point  C  is  egain  bisected  the  line  AB,  and  its  pro- 
longation AC,  form  a  straight  line;  if  not,  choose  a  point  midway 


Elem.    of  surv.    1A  ..ssignnent  9  Page   13 

between  C  and  the  point  C'   next   it;   this  mid-point  will   lie  in  the 
prolongation  of  A3,   as  required.      In  the  above  method   oy  douole- 
eighting  it  is  assumed  that  the  vertical  axis   is  truly  vertical 
and  that  the  horizontal  axis   is  truly  at  right  angles  to  it. 

(Sec.    Adjustment  of  the   Transit,   Assignment  XIV.) 


(90)   b_,    MEASURING  HCHlZOFL-iI 

The  transit  is  used  to  measure   angles   in  the  horizontal 
plane.      These  angles   are   the   bearings   of   lines,    deflection  angles 
for  change'    of  direction,    azimuths  from  any  assumed  point   of  di- 
rection,   or   mgles  included  between  any  two  lines,  and:  hence  directly 
the  interior  angles  of  any  concavs  figure,   as   those   of  a  triangle 
or  other  polygon  in  a  horizontal  plane. 

(a)  To  measure  angles  of  bearing* 

Set  up  the  transit  over  one  extremity    of  the  line;   set  the 
vernier-index  (that  of  the    A  vernier)    on  zero  of  the  graduated 
plate.     With  the   alidade  plate  clamped   in  this  position,   and  the 
lower  motion  screw  undamped  direct    the   line   of  sight   in  line   of 
the  assumed  meridian  (magnetic,  true,   or  any   other  chosen  meridian), 
Y.OVT  clamp  the   lower  motion  adjusting  by  means   of  the   lower  tangent 
screw.     Unclamp  the   alidade-plate  and  sight  on  a  rod  or  marker  hedd 
on  the  line  whose   bearing   is  required  and  rtad  the  angle  moved  over 
by  the  vernier   index.      This  will  be  the   angle  _of  bearing.      (Compare 
this   method  v.-itii  th?t   explained  in  Compass   Surveying,   Assignment  \I.) 

In  rending  the   an^ie  always  note  carefully  the  direction  in 
which  the  vernier   index  raovss   snd  observe  the  numbering  on  the  piste 


Fler.    of   Surr.    1A  Assignment   y 

for  this  mcvetrent  -  the   inner  eet  of  figures  on  the   limb,    if  the 
irovement  is  clockwise;  the  outer  set  of  figures,    if  the  movement 
is  cour.ter-clocln.vise.      The  bearing.,   would  be  recorded  as  N  23°12'E, 
or  K23C12'W,   or  as  S25°12IE   (or  W)    as  the   case  may  be.     Bearings 
must  always  be   so  designated.      (See  Compass  Surveying.) 

(b)    To  measure   a  deflection  angle; 

Set  up  the  transit  over  one  extremity  of  a-   line  A.     With  A 
vernier  set   at  zero  of  the   limb  and  the  alidade-plate  clamped, 
plunge   the  telescope    i^i.e.    invert  from  its  normal   position,  which 
means  vic,h  the   eye-end  near  the  A  vernier).     With   the  telsscope   in 
this    inverted   position  sight  upon  a  marker   (a  rod,   pin,   or  stake) 
held   at  the  other  extremity  cf  the    line  B,  the   lower  motion  being 
used  for  this  purpose.      Clamp  the  lower  motion  and  by  means  of  the 
tangent -sere*1'  of  the   lower  notion  bisect  the  marker.      Turn  the 
telescope  back  to  normal,      she  line   of  sight  is  now  in  the  prolonga- 
tion of  the   line  jlB.     Unclamp  the  alidade-elate,   sight   in  the  di- 
rection of  the    deflected  line  AC;  clamp  the  upper  plate  and  bring 
the   line  of  sight   exactly  upon  the  point   selectea  in  AC;   i.e.    bi- 
sect  it.      Kead  the   angle  and  record  its  deflection  as  right  or 
left    in  accordance  with  the   movement  of  the   alidade;   thus,   Deflection 
18°27I  R  (right),    er  Defi.    i8°27'   L  (left),   ps  the  case  may    oe. 
It   is  al.rays  essential   that    the  designation  right   (R)   or   left   (L) 
ge  given   in   registering   deflection  angles. 

The  further   uses   of  the   transit  will  be  continued   in  the 
next  assignment. 


Elem.    of  fcurv,    1^  Assignment  9  Page   15 

QUESTIONS 

1.  l\iame   some  advantages   in  the  use   of  the  transit  as  coir.- 
pp. red  to  the   corapass. 

2.  A  vernier   is  constructed  by  dividing  49  thirty  minute  di- 
visions into  50  equal  parts;  what  is  the   least-count  of  tnis 
vernier?  (<yln  degrees?  (b)    in  minutes?    (c)   in  seconds? 

3-  By  a  figure  neatly  and  carefully  drawn  show  what  you 
understand    Dy  flauble   sighting  as  given  in  paragraph  89  in  this 
as  e  ignment . 

4-  The    deflection  angles  of  a  survey   of  closed  traverse  are 
as  follows:     42°16',    1110!?1,    118°45',    87°40'.      (a)  What   is  the 
enr.ular   error   of  closure?      (b)  Distribute  the  error  to  the    least 
ti«/o  angles   and  give  the   vclue   of  the    interior  Angles   of  the    field. 

References  : 

Tracy,   Chap.    XI. 
Raymond,    pp.    100  -   110. 
Johnson,    pp.      93   -   100. 

dreed  &  Hosmer,   Vol.    I,   Chap.    III. 


"JKlVFRoIl'Y  OF  CAUFORNlA  EXri.I^lON  DIViSIOK 

Correspondence  Courses 
Surveying-lA  Elements  of  Surveying 

Assignment,  10 
The  Transit  and  its  Uses 

31)  RARGDiG  LINES  MD  kEASURIHG  ANGLES 

The  varied  uses  of  the  transit  in  surveying  and  engineering 
rest  upon  two  principal  functions,  the  sighting  of  straight  lines 
and  the  measurement  of  vertical  and  horizontal  angles.  This  assign- 
ment therefore  will  deal  with  a  f ev;  of  the  fundamental  uses  of  the 
transit  in  ranging  lines  and  measuring  angles.   A  knowledge  of  these 
fundamentals  will  enable  you  to  employ  the  transit  for  many  other 
uses. 

A  line  is  said  to  be "ranged  out"  when  a  line  segment  or  any 
t',vo  points,  or  a  known  point  and  the  line-direction  are  given.   If 
a  line  segment  is  given  and  it  is  required  to  extend  this  line  in 
either  or  ooth  directions,  the  method  is  usually  the  same  as  that 
explained  in  the  preceding  assignment.   Set  up  the  transit  over 
any  point  in  the  segment;  sight  on  a  marker  placed  on  any  other 
point  in  the  segment;  clemp  both  plates,  and  fix  other  points  in 
the  line  by  sighting  through  the  telescope.   If  it  is  required  t,o 
extend  the  line  both  forward  snd  backward,  after  sighting  points, 
say  in  the  forward  direction,  plunge  the  telescope  and  proceed  in 
like  manner  in  the  opposite  direction. 

In  cace  two  points  are  given  conceive  these  as  the  termini 
of  a  line  segment  and  proceed  in  the  same  manner. 


Elera.  of  Surv.  1A         Assignment  10  Page-  2 

Given  a  point  in  a  line  and  the  angle  of  direction,  i.e.  its 
bearing  or  direction  with  respect  to  some  other  line  of  fixed  po- 
sition.  Let  the  point  be  A  and  the  angle  c<  .   Set  up  the  transit 
at  A;  with  vernier  eet  at  0,  turn  on  the  lower  Motion  until  the 
line  of  eight  is  on  the  line  of  known  direction  by  sighting  at  any 
point  in  the  known  line  other  than  A;  clamp  the  lower  motion;  un- 
clr.mp  the  upper  motion  (the  alidade  plate);  turn  off  the  angle  b< 
(right  or  left  as  the  caee  iray  be),  making  the  final  more  delicate 
adjustment  with  the  tangent  screw.  The  telescope  is  now  in  the 
line  required;  that  is,  its  direction  and  one  point  (A)  are  deter- 
mined.  Place  a  marker  to  fix  upon  the  ground  the  new  line  thus 
determined. 

In  ranging  out  railroads,  wagon  roads,  canals,  ditches,  and 
in  fact  almost  all  lines,  the  lines  are  broken  and  are  formed  of 
many  segments  of  greater  or  smaller  size.  When  such  a  series  of 
lines  is  run,  the  road  is  eaid  to  deflect  (right  or  left)  at  certain 
designated  points  in  the  general  route  of  the  road.   In  running 
these  segments,  therefore,  it  is  necessary  to  set  up  the  transit 
(or  occupy)  each  point  where  a  change  of  direction  or  deflection 
takes  place.   The  transit  telescope  is  then  brought  into  line  with 
the  last  segment,  the  upper  motion  being  clamped,  and  the  lower 
notion  left  free  to  turn.  The  deflection  angle  is  then  turned 
off  with  the  upper  plate  undamped.   In  this  caee  the  final  and 
nice  adjustment  should  be  mad&  by  means  of  the  vernier  and  tangent- 
screv.   The  new  segment,  or  such  portion  as  can  conveniently  be 


El em.  of  Gurv.   lA         Assignment  lu  Page  3 

sighted,  is  then  established  and  the  work  can  proceed  to  the  next 
etation  or  point  of  change  of  direction. 

To  bring  the  telescope  in  line  with  any  previous  segment, 
after  setting  up  over  a  point  at  which  deflection  takes  place,  it 
is  the  best  practice  to  proceed  as  follows:  Clamp  the  alidade  plate, 
fixing  the  vernier  at  zero;  unclanp  the  lower  plate,  plunge  the 
telescope,  and  backsight  on  a  point  in  the  segment  just  established; 
now  clamp  the  lower  plate  end  return  the  telescope  to  normal  po- 
sition (i.e.  re-plunge  it).   It  is  now  pointing  in  the  direction 
of  the  last  segment  prolonged  through  the  point  occupied  by  the 
transit.  **ow  turn  off  the  deflection  angle  on  the  graduated  plate 
and  proceed  as  in  other  cases. 

This  method  requires  tnat  the  transit  be  in  perfect  adjust- 
ment and  especially  that  the  horizontal  axis  of  the  telescope  be 
truly  horizontal  and  at  right  angles  to  the  line  of  collimation 
of  the  instrument.  (See  chapter  XIV  on  Adjustment  of  the  Transit.) 
To  avoid  error,  in  case  these  conditions  do  not  obtain,  the  fol- 
lowing simple  method  may  be  substituted  for  the  latter  favorite 
method;  With  alidade  plate  clamped  (vernier  at  zero^  and  telescope 
normal,  sight  in  a  backward  direction  to  the  previous  segment; 
then  add  180°  to  the  deflection  angle  and  turn  off  this  sum  on 
the  graduated  plate'  with  lower  motion  clamped,   i'he  telescope  will 
then  be  in  line  of  the  new  segment  as  before.   (Caution,  be  sure 
that  the  angle  turned  off  is  the  euni  of  180°  plus  the  deflection 
angle  and  that  the  limb  is  read  in  the  proper  direction.) 


Elem.  or  burv.  1A         Assignment  lo  Page  4 


(92)  MEASURING  ANGLES  WUh 

In  the  assignment  on  fhe  Compass  and  jts^  Uses  full  instruction 
was  given  on  measuring  and  setting  off  angles  by  means  of  that  in- 
strument.  i'he  degree  of  accuracy  secured  with  the  transit  in  such 
work  is  much  greater;  and  the  ease  of  setting  off  and  of  sighting 
by  aid  of  the  telescope  renders  the  transit  the  best  instrument 
available  for  such  work. 

The  best  forms  of  surveyor's  compass  are  capable  in  good 
hands  of  measuring  to  the  nearest  five  minutes  wf  arc  with  a  prob- 
able error  of  perhaps  one  to  two  minutes,  since  to  read  the  compass 
limb  to  5  minutes  requires  that  estimation  be  resorted  to  in  the 
last  analysis,   fhe  transit,  however,  in  its  best  foras,  is  capable 
of  reading  directly  to  the  nearest  ten  seconds  of  arc,  and  oy 
methods  in  usa  by  the  skilled  engineer  a  really  good  transit  may 
give   reliable  determinations  of  angles  to  the  fraction  of  a 
second  with  a  probable  error  of  perhaps  one  tenth  to  two  tenths 
of  a  second. 

It  is  only  in  the  most  refined  measurements,  hov.ever,  that 
any  such  decree  of  accuracy  is  required,  most  work  being  sufficiently 
close  when  readings  of  angles  are  made  to  the  minute  of  arc.  But 
this  is  easily  attained  by  means  of  the  transit,  most  instruments 
reading  directly  to  the  nearest  minute  on  their  verniers,  and 
some  to  10  seconds.  By  the  method  of  repetition  (explained  further 
on  in  this  assignment)  the  refinement  may,  if  desired,  be  carried 
to  T/ithin  a  fev,'  seconds. 


Elem.    of  Surv.    1A  Assignment,  10  Page   5 

As  an  exercise   in  transit  use  in  reading,  angles,    set  up  the 
instrument  over   some  point,   A,  with  alidade  plate  clamped  and  lovrer 
undamped,   sight  upon  sou.e  point  B,  clamp  the    lower  notion,    and 
bisect  B   by  means  of  tangent  screw.     g,ead  the   limb  of  the   graduated 
plate  to  the  nearest  division  as   given  by  the   vernier   (you  should 
already   have  determined  the   least  count  of  thb  vernier).      Unclamp 
the  graduated  plate;   sight  upon  a  third  point,   C;  clamp  the  gradu- 
ate-:   plate  and  bisect  this  point  by  means   of   its  tangent  screw; 
anc   read  the   linb  as  before.      The  difference  between  the  two  read- 
ings will  be  the  angle  BAC.      This  measurement  should  now  be  checked. 

This  ie  done  by  unc lamping  the  alidade 
plate  and  again  bisecting  point  B.      The 
C       limb  should,   obviously,  have  returned 


Fig.    27  to  its  former  position  and  the   first 

reading  made  above   should  appear  on  the  plate.      If  so,   we   say  the 
angle    "checks"  and  hence  we  can  put  more    reliance  upon  our  work. 
This   is  a  very  simple,  yet  effective,   means  of  verifying  your 
readings  of  angles,  which  should  always  be  resorted  to  where  time 
or  expense  is  not  too  great.      Other  methods  of  a   more  elaborate 
character  are  often  employed  for   cheeking  angles;  these  will  be 
explained  under    "Measuring  Angles   by  Hepetition". 

(3)   TRAVERSING 

Lines  and  angles  measured  one  after  another   by  compass  or 
transit  are  said  to  be  traversed;  that  is,  the  whole  series  of 
lines  of  a  road  or  field  are  gone   over   in  order,   by  measuring 


Elera.    of   £>urv.    1A 


Assignment   10 


Page  6 


lengths  with  chain  or  tape  (or  by  stadia)  and  taking  angles  by 

instrument.   We  have  already  explained  traversing  by  means  of 
compass  and  chain  in 
^Compass  Surveying.   Traversing  by  means  of  transit  and  tape  will 

be  explained  here.   And  while  in  case  of  compass  work  the  chain 

gave  sufficient  accuracy  of  line  measurement,  a  more  exact  or 

refined  set  of  determinations  is  secured  by  use  of  transit  and 

tape.   A  steel  tape  with  graduations  in  feet,  tenths,  and  hundredths  of  feet 

is  most  suitable  for  use  with  a  transit  reading  angles  to  minutes 

and  even  seconds. 

Traverses  are  of  two  classes:  open,  such  as  lines  of  wagon 
road,  street,  railroad,  canal,  etc.;  ana  closed,  such  as  fields 
of  various  polygonal  forms.   In  the  latter  the  traverse  is  said  to 
cloee,  if,  after  having  gone  completely  around,  the  last  point  as 
determined  by  measured  sides  and  angles,  falls  exactly  at  the  point 
of  beginning.  As  this  is  seldom  the  case,  there  is  then  a  greater 
or  less  degree  of  "error  of  closure'  caused  either  by  measurement  of 
lines  or  measurement  of  angles,  or  by  both,  the  presumption  being 
that  errors  arise  from  the  two  sources. 

The  detection  and  adjustment  of  errors  due  to  both  causes 
are  not  so  easily  made  in  open  traverses  as  in  those  which  by  their  very 
nature  c?Qse. 

fscT^r 

c 


Figure  28 


Elem.  of  Surv.  IA 


Assignment  10 


page  7 


Figure  29 


A  line  of  road  starting  at  A  and  ending  at  F  v.lth  deflections 
at  B,  C,  D,  E  (Fig.  28)  will  afford  no  such  check  as  that  of  closure 
to  be  found  in  case  of  a  field  of  the  form  (or  any  other  form)  shown 
in  the  accompanying  figure  (Fig.  29).  Here  is  shown  .what  may  graph- 
ically represent  an 
error  of  closure  M'M 
which  is  a  line  in 
magnitude  and  direction 
sufficient  to  close 
the  polygon.  Evidently, 
if  the  sum  of  the  de- 
flection (exterior) 
angles  be  greater  or  less  than  360°,  error  is  manifest,  but  may  be 
due  either  to  line  measure  or  to  angle  measure,  or  to  both.  Such 
error  is  usually,  in  practice,  distributed  by  proportion  to  the 
sides  and  angles  so  as  to  satisfy  conditions  and  cause  the  figure 
to  close  in  fact  as  well  as  in  theory.   The  manner  of  dealing  with 
this  phase  of  the  problem  will  be  treated  in  Assignment  XVI  on 
Land  Surveying. 

94)  DIFFERENT  WAYS  OF  ioEASUKMG  ANGLES 

If  we  consider  any  closed  figure  bounded  by  straight  lines 
the  angles  of  which  it  ie  desired  to  measure  with  a  transit,  there 
are  four  ways  in  which  this  may  be  done.  The  method  chosen  is  a 
matter  of  convenience,  as  the  same  results  may  be  accomplished  by 
any  one  of  the  four. 


Elem.  of  Sur-r.  1A          Assignment  10  Page  8 

In  traversing  a  polygonal  figure  the  exterior  angles  may  be 
measured  one  by  one,  which  amounts  to  a  measurement  of  the  deflection 
angles  in  order  around  the  field.   The  interior  angles  at  each  cor- 
ner may  be  found  by  subtracting  the  exterior  (deflection;  angles 
from  180°. 

In  another  method  the  interior  angles  may  be  measured 
directly,  thus  avoiding  a  troublesome  computation;  but  this  method 
is  not  so  commonly  used  as  the  deflection  method,  which  lends  it- 
self to  progressive  steps,  and  allows  the  records  to  be  easily 
kept  and  the  errors  checked. 

Another  way  to  accomplish  the  reading  of  angles  is  to  set 
up  within  the  figure  and  take  the  angles  in  series  by  sighting  to 
each  station  (vertex;  of  the  polygon  in  order.  This  is  best  done 
permitting  the  angular  measure  as  shown  on  the  graduated  circle 
-,o  accumulate.   The  closing  reading  \vill  be  the  initial  reading  plus 
30°  -  i.e.  a  perigon.  This  affords  a  ready,  although  not  an  ab- 
solute, check  upon  the  accuracy  of  the  work  and  in  some  cases  this 
method  is  to  be  preferred  to  others. 

The  fourth  way  of  making  angle  measurement  is  by  azimuths 
referred  to  sore  line  assumed  as  zero,  called  a  reference  line. 
This  reference  line  may  be  any  convenient  line,  as  a  bounding  line 
of  a  figure,  magnetic  north  and  south  line,  starting  from  either 
the  north  or  scuth  point.   Likewise  true  north  and  south  may  be 
made  the  line  of  reference,  by  convention  and  universal  practice 
azimuths  are  always  read  to  the  right,  i.e.  the  telescope  is  turned 


Elem.  of  Surv.  lA          Assignment  10  Page  9 

clock-vise;  but  either  the  north  point  or  the  south  point  (magnetic 
or  true  meridian)  may  be  the  starting  point  on  the  zero  azimuth. 
As  the  azimuths  are  conveniently  checked  fcy  means  of  the  magnetic 
needle  (an  adjunct  of  every  complete  transit),  it  is  well  to  taifee 
azimuths  from  the  magnetic  meridian.   In  making  astronomical  ooser- 
vations  for  aeridicn  (longitude),  latitude,  time,  etc.,  in  solar 
observations  or  upon  some  star,  it  is  beet  to  consider  azimuths 
with  reference  to  the  true  meridian  as  this  simplifies  computations 
and  is  the  general  practice. 

The  ccmpass  needle  may  in  this  case  also  be  used  for  checking. 
It  is  especially  convenient  when  the  compass  plate  is  furnished  vdth 
a  variation  arc  to  set  off  the  daclination  by  that  means  so  that 

the  "check  '  angle  may  oe  read  directly;  otherwise  it  will  be  nec- 
essary to  add  (or  subtract)  the  declination  for  each  reading -of 
angle. 

Every  line  has  two  azimuths,  the  forward  azimuth  (or  6 imply 
the  azimuth)  taker,  -.irith  transit  at  the  back  end  of  the  line,  and 
the  back  azimuth  taken  with  transit  at  the  forward  end  of  the  line, 
As  these  two,  azimuth  and  b?ck  azimuth,  differ  by  180°,  the  back 
azimuth  of  any  line  whose  azimuth  is  known  may  be  had  by  adding 
(or  subtracting)  180°  from  the  azimuth,  or  vice  versa. 

Orienting  the  instrument  is  an  operation  that  is  fundamental 
in  taking  azimuths.   This  consists  in  bringing  the  line  of  sight, 
with  plates  clamped  (the  alidade  plate  and  its  vernier  preferably 


Elera.    of  Surr.    1A  ^.s^Ignment  10  Page   10 

at  zero)    into  parallelism  with  the    line  of  reference,    i.e.  to 
zero  azimuth.      Thit   orientation  is,   hence,  the  first  step  in 
measuring  angleE  by   azimuths. 

There  are  two  ways  of  taking  azimuths  with  the  transit,      in 
one  the  back-sight  is  taken  with  telescope  plunged,    and  the  other 
the  telescope   is  always  normal.     Both  methods  have  their  advantages 
and  di sad-vantages.      The  first  method  (plunging  telescope  for  back- 
sights)  does  not   require  a   setting  of  the   vernier  after  orientation; 
with  the    second  niethod    (telescope  normal),    the  vernier  must  be  re- 
set for  each  angle.      This  latter  operation  is  troublesome  and  is 
likely   to  introduce  &  snail  error  caused  in  setting  the  vernier, 
which  may,  hovrever,    be  jaore  or   less  compensated.      Xhe  t>ac£-azizautii 
may  always   be   obtained  by  adding  180°  to  the  azimuth  -  a  check  that 
should  be  automatically  applied  vhether  recorded  or  not.      If  the 
transit   is   in  adjustment  as   regards   its   line  of  colliraftion  and  if 
the  horizontal  axis  is  truly  horizontal  and  at  right  angles  to  the 
lins  of  eight,   the  first  method  is  preferable.      (See  Assignment 
XIV  on  Ad  justnents  ol_  the_  Iransit. ) 

55)   AI'iCrLLS  BY  i-^HLTKIOl* 

io  measure  angles  when  great  refinement  is  required,  or  when 
it  is  desired  to  "check"  angle  readings  effectively,  the  method 
knovm  as  "Measuring  Angles  by  Kepetition"  is  resorted  to.   This 
consists  in  turning  off  tne  given  angle  between  any  two  lines  again 
and  again  from  two  to  six  times  or  more,  and  adopting  the  mean 
(average)  of  such  readings  ae  the  true  or  recorded  angle.   To 


Flerr..  of  Surv.  1A          Assignment  10  Page  11 


\          / 


illustrate:     Suppose  the  angle  XOY  in  the  adjoining  figure  is 
X\  /  'i       sought.     With  transit  at  0  and  graduated 

plate  clanped,  vernier  at  zero,   orient  the 
instrument   on  line  OX  by  bisecting  X.      Clamp 

lower  plate,  unclamp  e.lidade  plate   avd  sight 
0 

Y,  carefully  bisedting  with  tangent-screr; 
Figure   30. 

read  angle  measured.      Ihis   is   (approximately) 

the  angle  XOY.      Now  repeat  the  angle  measurement  say,  five  times, 
thus:     Without  disturbing  the  upper  motion,   release  the   lower 
clamp-screw  and  turn  telescope  bock  to  X,  making  the  necessary 
fine  adjustment  in  bisecting  X  by  means  of  the  loger  t&ngent- screw; 
unclarap  the  upper  pl^te  and  again  bisect  Y.      Clamp         the  upper 
ple.te  when  in  that,  position  and  ::iake  the  fine  adjustment  with  the 
tangent-screw  ae  before.      Ihis  is  the  first  measurement.      It    is 
irnmaterial  whether  "ve  re-read  the  angle  at  each  measurement  or  not ; 
in  practice   it  is  not   so  read.      Now  by  means  of  the  lower  motion 
sight  back  on  X,   then  by  upper  motion  sight  on  Y  (second  measurement) 
and   so  continue  until  the  angle  has  been  repeated  five  times; 
i.e.    called  six  repet  itione.     Evidently  an  accumulated  angular 
quantity  six  timee  the   angle  XOY  (as  observed  at  the  first  reading) 
h?s  beer,  turned  off  on  th~=  graduated  plate.      This  accumulated 
quantity  divided  by   six  gives  the  angular  value  of  angle  XOY>  and 
if    the   instrument  has    been  manipulnted  with  care  and  the   points  X 
and  Y  exactly  bisected  in  each  setting,  the  value  for  the  angle 


thus  obtained  is  much  less   liable  to  error  than  would  be  the  single 
first  reading  or  perhaps  ar§r  lesser  number  than    six  repetitions. 


Elem.    cf   Surv.    J.A  Assignment  10  Page   12 

Furthermore  the  transit  ar.d  vernier  are  graduated  to  read,    say  to  one  min- 
ute of  arc,    but  by  this  method  it  is  possible  to  measure  the   angle  to  within 
a  few  eec ends  oi  arc,    since  by  the  accumulation  of   small   differences, 

practically  impossible   of  dstection  in  observing  the  vernier,   the 
total  difference   is  by  division  distributed  in  the  average,    thus 
giving  a  more  truly  correct  determination. 

In  further  illustration  let  us  assume  that  the  angle  XOY 
by  first  measurement  was  £3°17',    b^   the   first  repeating  46°35!. 
Here   evidently  the    I/1    of  the   first  determination  was  slightly 
under  the  mark.     While   at  the   tnd  of  the  fifth  repeating  (for  the 
six  repetitions,  as  ?/e   say)  the  total  angular  quantity   read  upon 
the   plate   is   139°  45';  wh  ich  now  c'ivided  Dy   6  gi\es   23n7'30"  as 
the  most  probable   value  of  an^le  XOY.      And  this    seams  tc  have 
been  revealed  oy  the   second  reading,   but   it  is  accepted  with 
greater  assurance  from  the  evidence  cf  the  six  repetitions. 

The  student  is  urged  to  acquaint  himself  vith  this  method 
of   "reading  angles  by  repetition",   both  theoretically  and  prac- 
tically,  as  it  furnishes  the   engineer  his  greatest  reliance   in 
angular  measurement.      It   is  especially  useful  where  the  degree  of 
accuracy    sought  exceeds  the   limits  of  plate   md  vernier  graduation, 
and  is  a  most  reliable  'bheclc"  even  vrhere  the  greater  degree  of 
refinement   is  not  desired. 

References : 

Breed  &  riosmer  pp.    105,    108,    109-111,  Vol.    I. 
Tracy  pp  152-156 

hayraoad  pp.  102-105 

Johnson  pp.    93-   98 


Blera.    of  Surv.    1A  Assignment   10  page  13 

Exercises  in  Transit  Use 

1.  Stake  out   a  quadrangular   field  by  pacing,   no  side   less  than 
150  feet.     Assume  zero  azimuth  to  be  magnet ic-Jiorth.      Set  up  at 
most  westerly  corner  aid  measure  the  azimuth  of  each  side  by 
either  method   of  taking  azimuths.     Record  the  magnetic  bearings 

as  a  check  against   large  ecrors  in  angles. 

2.  Lay  out  upon   the  ground  a  triangle,    sides  approximately 
150  feet;  not  an  equilateral   triangle,   but  no  angle   less  than  30° 
nor  more  than  120°. 

Measure  each  angle  by  repetition,   making  six  repetitions 
with  telescope  nonr.al,   beginning  with  A,  vernier  set  at  0°,     Then 
with  telescope  inverted  ootain  angle  by   six  repetitions,    starting 
with  rernier  set  at  270°.      Check  each  set  of  readings.      Also  check 
by  taking  the   sum  of  interior  angles. 


UNIVEKLJT.;  01    Cr.IT/CFdJA  FXiTN^TON  DIVISION 
CGRRLSPuKOLK'Cb  CGl'rteEb   IK  £NOIii!r.,U<.I;'G   CU3JECTS 


Course    1A  Zl.  exeats   o:?  Survey  ing  Swafford 


OBbERVP'iu  ?VK  j^ijHA]*  ^{D  LA^/CJl'E 

FOREWORD  : 

This  assijnnent  will  treat   oi  the    several  methods  employed 
by  surveyors  in  locating  the  North  and  South  line  through  any  po- 
sition on  the  earth  and  also  of  determining  the  surveyor's  angular 
distance  north  or  gjuth  of  the  equator.      These  comprise  the   sur- 
veyor's co-ordinates  upon  the  earth's   surface,   which  fix  his  po- 
sition;  in  relation  to  these  the  direction  and  course  of  all   lines 
in  surveying  are  run. 

56)   PRELIMINARY  CONSIBEkAlIGNS 

A  few  definitions  and  explanations   are  necessary  at  this 
place,    in  order  that  certain  terrrs  and  famdarr.ental  facts  relative 
to  the   subject  may  clearly  be  understood 

Leridian  is  &  term  applied  to  the  north  and  south  line 
passing  through  any  gi\en  point  upon   the.  earth's   surface.        ine 
term  is  also  applied  to  a  great  circle  of  the  celestial  sphere 
mafle  by  the   intersection  of   a  pl&ne  pa&sing  through  the   observer's 
north   and  south  points  (the  uorth  and   south  points  o^'  the  neavens) 
and   including  the   zenith  and  nadir,      such  a  plar.e  passing  through 
the  earth  determines  a   great  circle    of  that   uody.      The   center  of 
the  circle    is  the  center  of  the  globe  end  the  circle    Is  the  troce 
of  the   plane  where  it  cute  the   earth's  sphere. 


.    of   ourv.    1*.  Assignment    11  Page   2 

Only    In  changing  position  in  a  rorth  end  soutn  line  does   one 
me  intain  .the   same  meridian,    as  any  slightest  movement  to  east  or 
west  causes  change  of  r-ieridinn  ;  hence,   for  any  position  upon  the 
earth's  surface   there  c?n  be  one  and  only  one  meridian. 

Should  a  Eur\eyor  ^.ovt  alon£  his  raeridiJn  northward,   he 
would  approach  the  earth's  north  pole,  the  point  or.  the  surface 
pierced  by  the  axis  of  rotation.      tSo  also  if  he   should  proceed 
southward  lie  t. ould  eventually  reach  the   south  pols.      Midway  be- 
tween these  two  polee   liss  the   equator  -  ninety  degrees  from  either 
pole. 

The  Equator   is  a  great  circle  upon  the  surface  of  the  earth 
formed  by  a   plane  -which  passes  through  the  center  of  the  earth  at 
right   angles  to  the  axis  of  rotation.      Later   it  will  oe  necessary 
to  distinguish  the  earth's   equator  from  the  celestial  equator,   but 
in  the  present  consideration  the  distinction  is  not   of  importance. 

Since  there   ie  no  natural  fisced  point  taken  in  an  east  and 
west  direction  upon  the  earth's   surface,    a  certain  rceridian  is 
chcsen  i'or  reference  callec1  a  prime  meridian,  notably  that  passing 
through  Greenwich,  England.      This   is  commcnlj    used  by  astronomers 
am?  navigators  for  convenience   in  reckoning  distances  east  and 
west  and   for  purpose?  of  t ime  or  longitude .      Longitude  and  time 
are   expressed  either   in  decrees,   minutes  and  seconds   of  ?.rc  or  in 
hours,  minutes,   and  seconds  or  time;     these  units  oeing  readily 
convertible,    one  into  the  other- 


Elera.    of  Surv.    1A  Assignment   il  Page  Z 

prirv 
Cther^iueridians     are  also  used,   as   taris   by  the   French; 

Berlin  by  the  Germans;  bt.    Petersburg  oy   the  Russians;   etc.      In 
the  United   States  we   occasionally  mate  use  of  the  meridian  oi 
Wcshington,  D.C.    ss  a.  prLue    reference;    oat  since  this  causes   some 
confusion,    it   is  better  for  many   reasons  to  adhere  to  Greenwich  as 
the   one  prime  meridian.     We  rill 'always  do  so  in  these  assignments. 

Lon£itud_e  is  the   di  stance-  either  -east  or  Tsrest  of  the  prime 
neridian  expressed  either   in  degrees  or  hours;   commonly  in  degrees 
by  the   surveyoc  an,:   hours  by  the  navigator.      Furthermore,  the 
longitude  extend e   l£jo  on  either   side  of  the  piime  meridian  and 
is  expressed  as  so  many  degrees  east   longitude   or  west   longitude. 

Latitude  is  distance  north  or  south   of  the  equator,   measured 
in  degrees  off-arc   on  the  meridian   at  any  given  place.      As  the 
equator   is  at  quadrant  distance  from  either  pole  the  range   of 
latitude  is  from  0°  at  the  equator  to  90°   at  the  poia.      Correspond- 
ing to  terrestrial  latitude  is  celestial   (astronomical^    latitude 
conceived  as  measured     upon  an  arc   of  the  celestial  sphere.     We 
also  use  the  measure   of  pqlar  distance   or  cc- latitude,   v.'hich  •  »» 
is   the  complement   oi   the   latitude. 

Since  the  fixing  of  the    observer's  position  by  means   oi 
these  co-ordinates,    latitudes  --nd   longitudes,    is  al./ays  oi   j..rune 
importance,  we   shall   proceed  to  explain  how  they  are  deter:nin>"d. 

If  we  could  sie,ht  upon  the  north  or  south  pole  of    the  earth 
and  also  lay  off  arc   distances  upon  a  meridian  upon  the   earth's 
surface   directly,   v/e  :.iight   have  a.;i   ideal  method   oi    observation. 


Elen.    of  3urv;    lA  Assignment    11  Page  4 

But  this  method   is   impossible.      Cth&r  i..etLods,    however,    accomplish 
our  purpose  even  better  than  thnt  of  direct  measurement. 

The  sun  and  the  fi::ed  stnrs  afford  us  a  means  of  determining 
meridian   and   latitude   chat  is  •available  at  all  times  v;her.  the   sky 
is  clear  enough  to  observe  them.     Especially  favorable  for  this 
work  is  the   sun,  which  may  be  viewed  by  day,   and  the  Pole  Star 
(Polaris),   Which  is  generally  visiole   in  thenorthern  hemisphere 
at  night.      Other  stars  may  be  used,   but  our  7vrork  will  be   limited 
to  the  methods  of   observing  upon  these  fvo. 

On  any  clear  night  you  may  see  Polar i£,    a  star   of  tha  fifth 
magnitude,   with  vhich  all  are  more  or   less  familiar.      It,   is  readily 
distinguished  by  being  in  line  with  the  tv;o  extreme   stars   of  greater 
magnitude   in  the  bowl  of  the  Dipper   (Constellation  of  Ursa  Major). 
On  the  opposite  side   of  the  Pole    Star,   aaout  equidistant  to  the 
Dipper,    is  another  constellation  shaped   like   the    letter  \'i  or  1L 
(Sigma  of  the  Greek  alphabet;;  this  is  the  constellation  Cassiopeia, 
and  these  constellations  are  of  great  convenience   in  locating  and 
determining  just  the  phase   in  v;hioh  Polaris  (the  Pole   Star;  may  be 
at   any  given  time.      Thest   seers  cnartec  as  here  shown  enable  us  to 
locate  the   celestial  north  pole,    i.e.    the  point  which  the  &xis  of 
the  earth  prolonged  would  pierce   if  extended  in   space   indefinitely. 
For  Polaris   is   quite  near  the  pole  (1°07'20")  and  is  no'?  approaching 
nearer  and  nearer  to  that  position. 

This  star  revolves  about  the   pole  'once   in  twenty -four  hours, 
and  trrice   in  that   period  of  time   it   is   exactly  on  the-   meridian,    once 


Lien,    of  3urv.    lA 


Assignment   11 


Page   4a. 


«///"> 


-A  c  "7 


Cassiopeia 


611 


}*  Polaris 
Xp-rie 


<3 
^ 


i'ca  f'ajcr   (Big  Dipper) 


Polaris  at  Upper  Culmination 
Turn  Chart  to  agree  with  Stars'  Positions 


Figure  31 


El  em.    of  Surv.    IA.  .         AtSi&nment   II  Page     5 

above  the  pole   (upper  culmination)  and  cace   Delo?;  the  pole  (lowe.r 
culmination).      In  that  time  also  it  is  once  at  the  extreme  right 
(eastern  elongation)   and  oiwe  at  the  extreme   left   (western  elonga- 
tion).     TAihsn  the  conditions  anci  ti.aes  are  favorable  it  is  very 
convenient  to  observe  upon  Polaris  \.rhen  in  one  of  the  four  positions 
or  phases   given  above,    i.    e. ,  at  either  upper  or   lower  culmination 
or  at  eastern  or  western  eloagati.cn,    as  the  necessary  computations 
for  determining  meridian  or  latitude  are  somewhat  simpler  than 
those  required  when  observation  is  made  at  any  other  time. 

Mote  on  the  ac9ompauying  chart    the  relative  positions  of 
the  pole,   Polaris,  and  the   stars  in  the  two  constellations,  the 
Dipper,  and  delta  ($  )   Cassiopeiae.      Hold  the  chart  toward  the 
north  before  you  and  turn  it  counter-clockwise  observing  the 
phases  of  sulmination  and  elongation  as  thus   illustrated. 

Now  if  a    line  of  sight  be  directed  at  the  Pole  Star  the 
instant  it   is  either  at  upper  or   lower  culmination,   this   line  of 
sight  will   evidently  lie  in  the  plane   of  the  meridian,  since   each 
a  plane  passes  through  the  earth's  center,  the   zenith,   and  the 
north  pole,     Hence,  the  meridian  or  north  and  south   line  is  de- 
termined. 

Either  the  compass  of  the  transit  may  be  used  for  directing 
this   line   of  sight  and  also  for  transferring  this   line  to  the 
earth's   surface  where   it  becomes  cf  practical  use  tc  the    surveyor. 
Note  that  the  methods  here  to  be  descrioed  give  one   ia  reality 
the   zero  azimuth  of  Polaris  with  respect  ^o  the    observer's  north 
and   south  line  upon  the   earth's   surface. 


Elem.  of  3urv.  1A          Assignment  11  Page  6 

(97)  TC  OBSERVE  ON  POLARIS  iVITH  COMP-uSS  AT  CULMINATION 

Choose  an  open  space  unobstructed  uy  trees  or  buildings, 
extending  600  feet  or  more  northward,  on  a  clear  night  when  the 
northern  constellations  are  plainly  visible.   Let  the  time  chosen 
be  half  an  hour  before  the  time  cf  culmination  as  obtf.ined  from 
the  Nautical  Almanac  or  Ephemeris.   (A  brief  list  of  computed 
times  is  given  with  this  assignment.   For  oiher  times  you  may  .make 
your  o:vn  computations.   See  tables  at  close  of  this  assignment. ) 

bet  up  the  compass  over  a  steke  having  a  point  marked  upon 
it.  Direct  the  line  of  sight  through  the  slits  in  the  standards 
and  note  that  the  star  will  be  on  the  meridian  (say  in  upper  cul- 
mination) a  few  minutes  after  tne  line  joining  Sigma  (s)  Ursae 

( 

Majoris  and  Delta  (£)  Cassiopeiae  passing  through  the  star  is 
vertical,   i'he  compass  line  of  sight  is  now  in  a  north  and  south 
line  and  should  be  fixed  in  this  position.   A  forward  point  -should 
be  set  in  the  morning  light  when  a  etake  may  be  readily  placed. 

The  magnetic  declination  may  also  be  readily  determined  by 
reading  the  angle  msde  oy  the  needle  at  this  time.  A  line  joining 
the  stakes  is  the  true  north  and  south  line  lying  in  the  plane  of 
the  meridian. 

As  it  is  difficult  to  view  the  stars  (sigma  Ursae  kajoris, 
Polaris  and  delta  Cassiopeia*}  conveniently  through  the  standards 
of  the  compass,  a  modification  of  this  method  is  ^aede  as  follows: 

Suspend  a  long  plumb  line  with  a  heavy  bob  evincing  in  a 
bucket  of  water  to  prevent  its  oscillation.  Back  of  this  about 


Siem.    of  Surv.    1A  Assignment   11  page  7 

20  or  30  feet  place  a  board  upon  two  upright   stakes  four  cr  five 
feet  high  ,and  upon  this  ooerd  set  the  rear  standard,   rera-jved  from 
the  compass   for  this  purpose;  bring  the   slit   in  ths   standard,   the 
plumb  line,   and  the  star   in  line   as  described  -above  and  complete 
the    operation  in  daylight  as   before  directed. 

At  upge£     culmination  Foifrie   is  oest  seen,  while  at   lower 
culmination  the  details  of  adjustments  of  the   line  of  sight   ere 
mere  readily  Accomplished.     Uoth  observations  are  accompanied  by 
difficulties;  the   observer  must  judge  which,   under  given  conditions, 
will  give  the   best   results.      Much  will  depend  upon  the  character 
of  the  view  and  upon  the  state  of  the  ataosphere;   if  cloud  or  haze 
interferes  with  a  clear  view  at  lower  culmination,   choose  the   time 
of  upper  culmination  instead.      At  certain  times  of  ye£.r  and  at 
given  latitudes  one  or  the  other  of  these  culminations   is  invisible 
on  account  of  daylight  conditions,     The  hour  o±   the  night  when 
either  culmination  occurs  may   influence   one   in  selecting  the  best 
time. 

>)   CAUTIONS   IK   OBSERVING   OK  KSLAKI&  AT  CULMINATION 

As  the  star's  apparent  motion  is  at  right  r.ngles  to  the 
plane   of  the  meridian,    it  changes  rather   rapidly    >nd  it  is,   there- 
fore, necessary  to  be  alert,   prepared  beforehand,  and  to  clamp 
the  compass  plate  at  the  instant  the  star  is   on  the  meridian. 
Since  the  movement  of  the   star   is  westward  at  upper  culmination 
and   eastward  at   lower  culmination,   it   is  advisable  to  follow  the 
star   in  these  directions,   keeping  it  well   in  line  at  every  point 


Eleni.  of  Surv.  1A          Assignment  11  £kge  8 

of  its  path.   Have  everything  in  readiness,  ths  time  of  culmination 
exactly  computed,  and  your  watch  set  tc  standard  or  mean  solar  tine 
in  accordance  with  the  sort  of  time  chosen  and  for  which  the  com- 
putations have  been  made.   To  bungle  you;-  work  means  that  you 
must  wait  12  or  24  hours  for  a  second  observation. 


(99)  TO  OBSERVE  ON  POLARIS  A.T  ELONOAi'IOW 

The  transit  will  be  used  in  this  explanation  of  the  method 
of  observing  for  azimuth  of  Solaris,  although  the  compass  also 
could  be  employed.   The  transit  is  used  here  so  ths/t  you  may  com- 
pare the  two  instruments  under  similar  uses.   It  may  be  remarked, 
however,  that  the  transit  is  the  more  satisfactory  one  in  any  case, 

on  account  of  the  better  vision,  the  meane  for  finer  adjustment, 
and  the  ease  with  which  the  stat  maj  be  followed  and  especially 
located  at  the  critical  moment. 

Note  that  the  star  et  eastern  elongation  is  moving  upward 
and  will  so  appear  in  a  transit  with  erecting  eyepiece;  with  an. 
inverting  telescope  the  reverse  movement  is  seen.  Also  at  western 
elongation  the  opposite  is  true,  the  star  moving  downward  at  the 
extreme  position  to  the  left. 

The  time  of  eastern  elongation  occurs  6h  03.4m  after  iower 
culmination,  while  that  of  western  elongation  is  oh  54.6m  later 
than  upper  culmination. 

The : declination  (or  polar  distance)  of  Polaris  is  constantly 
changing,  since  the  star  is  approaching  the  pole  at  a  -varying  rate, 


Elem.    of  Surv.    lA  Assignment  11  Page   9 

which  is  now  about  18.  C"  per  yet.r.      In  consequence,  -che   ozimuih 
of  the  star   at  elongation  vr.riss.      The  formula  for   solution  of  the 

spherical  trisngle  obtained   fraa  data  of  the  observer's   latitude 

• 

(or  as  given  in  this  formula  the   co-latitude)   and  the  polar  dis- 

tance is: 

,  sin  Polar  dist,. 

siu  star  s  azimuth  at  e  long  =:  ^i"  ;"la"ti™d7  '  or' 


in   logs, 

log  sin  azimuth  =  log  sin  P.  D.    +  co-log  sin  eo-lat. 

Tables  giving,  the  azimuth  of  the  star   at    elongation  (eastern 
and  isrestern)   are  compiled,    a  brief  table  of  ti\is  nature  being  appeaded 
to  this  assignment,   ar.d  are  &  ready   means  of  obtaining  these  figures 

without   labored  computation.      1'he  engineer  in  practice  should  avail 

but 
himself  of  such  help6>Asince  the    student,  must  master  principles, 

he   should   forego  the  uee   of  ready-made   stuff  to  the  detriment   of 
sound  training. 

(100)   DIRECTIONS   IN  DETAIL  FOR   USE  OF  THE  I'RAN&IT  IN  THIS  OBSERVATION 
AT  ELONGATION 

A  short  time   before  the  st?.r  reaches,    say  eastern  elongation, 
set  up  the  transit  in  a   suitable  place  with  an  open  view  extending 
600  feet   or  more  to  the  northward-      Have   at  hand  a  ready   means  of 
illuminating  the  cross  hairs   in  the  transit,   and  by  shortening  the 
telescope,  focus  the  objective  and  adjust  the  eyepiece  upon  Polaris 
and  see  that  there   ia  neither  parallax  ncr  aberration  dus  to  im- 
proper adjustment  of  the  telescope.      Carefuil^    level  the   transit 
plates  and  clamp  the  alidade  plate,    setting  the  A  vernier  to  zero, 
using  the  tangent   screw.      Also  have   the  clamp  for  the   -vertical 


m.  of  3urv.  1A          Assignment  11  Page  10 

motion  lightly  set  so  that  the  telescope  nay  be  readily  transited 
(plunged).  The  vertical  cross  hair  is  the  one  used  in  this  ob- 
servation and  should  of  course  be  in  perfect  vertical  adjustment. 
As  the  change  in  azimuth  is  very  slow  compared  with  such  dhange 
at  culmination,  'there  will  be  ample  time  to  make  the  two  sightings, 
the  first  vrith  telescope  normal,  the  second  with  plate  reversed 
and  telescope  plunged,  thus  eliminating  any  slight  lack  of  adjust- 
ment. tie  careful  in  both  positions  to  see  that  the  star  appears 
to  "thread"  the  vertical  cross  hair,  which  will  be  with  an  upward 
movement  in  the  erecting  instrument  and  with  a  dxwnward  movement 
in  the  inverting  instrument  at  eastern  elongation,  the  case  v;e 
have  chosen  for  these  directions.   In  reversing  for  the  observation 
with  telescope  plunged  the  graduated  plate  is  undamped  and  when 
the  star  is  again  bisected,  or  brought  to  the  vertical  cross  hair, 
the  final  adjustment  is  made  with  upper  plate  tangent  screw,   if 
the  B  vernier  now  reads  exactly  zero  (that  is,  A  has  moved  through 
just  180°),  the  telescope  has  pointed  to  the  stars  at  elongation 
in  both  positions.   If  there  is  a  difference  in  th«  two  readings, 
A  vernier  and  B  vernier,  then  one  half  of  the  difference  must  De 
added  (or  subtracted)  from  the  A  zero  when  the  telescope  is  re- 
turned to  normal  position.   X'hus  the  instrumental  correction  has 
been  set  off  on  the  limb  and  if  now  the  aiimuth,  taken  from  the 


table  or  computed  from  the  formula  given  above  (sin  asimuth  =  -SHi  —  2±_£  —  -Jv 

sin  co-  latitude7 

be  turned  off  on  the  limb  to  the  right  -  the  telescope  moving  to 

the  left  -  the  line  of  sight  is  pointing  in  the  plane  of  the  meridian. 


Elem.  of  3urv.  1A          Asaigamcnt  II  Page  il 

To  establish  tha  meridian  line  on.  the  earth,  .line  in  a  for- 
ward stake  600  or  more  feet  aray  and  also  set  another  stake  under 
the  plumb  bob  point  of  the  transit.   These  two  points  determine  the 
meridian  line. 

,      The  cross  hairs  ma./  be  conveniently  illuminated  by  holding 
an  electric  torch  or  a  bulls-eye  lantern  reflecting  into  the  ob- 
jective tube.  To  effectively  do  this,  a  piece  of  glazed  paper  or 
tracing  cloth  through  which  a  central  opening  half  an  inch  in  diam- 
eter may  be  mounted  upon  the  objective  end  of  the  telescope  ;  set 
this  at  an  angle  of  approximately  45°  and  the  light  held  at  the 
side  will  be  reflected  downward  through  the  tube. 

(101)  CAUTIOwS   IN   OBSERVING 

In  general  the  cautions  given  for  observing  at  culmination 
apply  in  this  case.   In  addition  to  these  see  that  the  cross  hairs 
are  distinct  and  that  the  star  IE  sharply  defined  in  the  field  of 
view,;  also  that  the  reflector  described  above  does  not  interfere 
with  a  clear  view.  When  once  sighted  the  star  should  be  kept  in 
view  and  followed  as  closely  as  possible  by  means  of  the  tangent 
6crev.-8  both  in  azimuth  and  altitude.  As  before  stated  the  star  at 
about  the  time  of  elongation  does  not  change  in  azimuth  perceptioly 
for  some  minutes,  but  when  the  least  change  is  noticed,  cease  to 
follow  the  star  as  it  is  then  no  longer  t.t  (or  near)  elongation. 

(102)  TO  FIND  IHL  LATITUDE  OF  IhE  OBSEKVLK 

It  will  be  noted  that  at  the  equator  the  pole  of  the  heavens 
is  on  the  horizon;  also  as  the  observer  moves  northward  the  altitude 


Elera.    oi    Surv.    La  Assignment   11  Page   12 

of  the   pole  increases   in  exact  proportion  with  the   latitude;  at 
the  north  pole   oi    the  earth  the  celestial  pole  is  in  the  zenith; 
hence  the   latitude  at  any  point   on  the   earth's   surface   is  equal 
to  the  altitude  of  the  celestial  pole. 

Therefore,  with  the  vertical  circle  and   level  on  telescope, 
in  perfect  adjustment   (See  Assignment  XIV,   Adjustments  of  the 
Transit)   bieect  the  Pole  star  at   culmination  ,   either  upper  or 
lower.     Re?.d  the  angle  of  elevation  on  Vertical  Circle.     If  at 
upper  culmination,   subtract   the  polar  distance  of  the   star  and 
correct  for   refraction  in  altitude  as  given  in  the  table  appended 
to  this  lecture.      If  at  lower  culmination  add  the  polar  distance 
and  correct  for  refraction  in  altitude  as  before.     The  net  result 
in  either  case  is  the   latitude  of  the  place. 

(103)   CAUTIONS   Hi  OBSEhVlfoG  FOR  L/uITUDL 

Choose  the  time  for  beginning  of  the  observation  half  au 
hour  before  culmination  and  follow  the  star  for  a  few  minutes  at 
least  before  that  time,      faote  that  whereas  the  star  changes  rapidly 
in  ajirauth  at  culmination,   on  the  contrary   it  moves  very  slowly  in 
altitude  at  these  times'and   for  several  ninutes   before  and  after 
culmination  has  (approximately)   the  same  altitude.      Therefore, 
without  too  great  presumption,  the   observer  r..ay  use  considerable 
deliberation  in  sighting  the  star  for  latitude.      But   atmospheric 
refraction  causes  the  star  to  appear  higher  above  the  horizon 
than  it  is  in  reality;  hence,    do  not  neglect  to  reduce  the   observed 
altitude  by  the  amount  of  the  refraction.      Note  that  the  refraction 


. 


To    Determine    the    Azimuth   of     Polaris  at  Any    Given    Standard  Time 
To    Compute  Angles    AOC     and    NOD. 


J3ef  in  if  i<Jn  » . 


NESW 
N5 
Z 
POP, 


Plane  of  the  obsery«rs\o™ 
Observer's    meridian 
Observer's  xenith. 
Polar   axis. 
Plane  of  the  equotoi 
L-PON»ZOA    Observer's    latitud* 
East  and,  west  line 
Path  of  Polaris. 
Polaris  at  upper  culm,, 
Polaris  at  western  e|ora-> 
Polaris  at  lower    culrn* 
Polaris  at  eastern  elc    t 


EW 

U.W.S.L.E.. 

U 

W, 

L, 

t. 


o'L.OK'U.OA  Declination  of  Tola 
POU-POU.'TOS. Polar  distance  of  ?e.fi» 
SoJ  Azimuth  of  Polaris  otW.H 

50M  Azimuth  of  Polaris  ot  E  <• 

5,  Polaris  as  observed ath«  • 

SOD  Azimuth  of  Polaris  as  obi  m 

5)  Mean  &«n  at  observer  Ml 

mean  noon  • 
V,  Vernal  equinox  at  obs  ;cr 

local   mean  noon- 

V»  Vernal  equinox  when  "Po  it 

S£  Mean  Son  at  local  hou  m^i 

when    Polaris  i&  at  ,- 
AOB  "^  '5          Local  mean  time  when  lew 
AOVZ  Observer's  s'idereal  hr* 

when     Polaris    is   qt  ,• 

VtOA  -^  is        Observer's  sidereal  tie* 

ascension    of  oOserve  ipt 
when    Polaris  is  at    • 
V.OA  •*•  16          Right   ascension  of  m  n 

at  observer's  local  *IM 
VtOC  •*•  15  Right  ascension  of  PolM 
t - AOC •  VtOA  minus  V,OC.  Houon 

of  Polaris   at  5,. 
Bearing   of  Polaris  a  j(. 


b»NOD 

Note.  Right  ascension  is  measured  from  the  vernalMJ 
in  the  direction  WAE.K  up  to  2.4- hours.  Hour  or  en 
measured  from  the  South, A,in  the  directic  to 
up  to  t4-  hours. 

ELxam  pie  . 

Find    the  azimuth   of   Polaris     on    Apri)-' 
at    9:3O    P.M.,  Pacific    Standard   Tim*   r 
BerKeley, California.    Latitude,  N.  37* 
Longitude,      IEZ.*     15'    -4-Z."   W.    «   6*"     ">  ™    t? 


The  Celestial    Sphere. 

Known    Data. 

I.  From  the  observers  watch '.  Standard  time   of  observation 

of   Polaris  at  3,  i.e.  hour  angle   for  Standard  meridian  cor- 
responding  to    AOB    for    observer's    meridian. 
2.. From  the  nautical  almanac;  Right  ascension  of  the  mean  sun 

at  the  previous  Greenwich  mean  noon.  Tnis  corresponds  at 

the  Greenwich  meridian  to  the  s'idereal    hour   angle    V.oA 

for  the  observer's    meridian. 

Right  ascension    of   Polaris   at  S,. 

Declination   of    Polaris. 

3.  From   a  U.5.G.S.  map    or  b^   observation :  Observer's  latitude.     Right  ascension  of   mean    sun  «t 

Ci  .  .  Greenwich  mean   noon   on  Apf^-i^ife- 

.   r  .    .  Local   time    of    observation   is    sfand- 

Greenwich  Sidereal  time     at   Greenw.ch  mean  noon  egoals  Qrd  Vlme  ^  8h  mcr-,dlQn  mirio.,  9-3 

the  right  ascension  of  the  mean  Sun  at  Greenwich  mean  noon. 

Observer's  sidereal  time   at  observer's   local  mean  noon 
equals   right  ascension  of  mean  sun  at  previous  Greenwich 
mean  noon   plos  increase   m  right  ascension  during  the  mea*^ 
time  period  between  the   previous  Greenwich  mean  no*1*  and 
the  observer's   local   mean   noon.    Observer's   sidereal  time 
when    Polaris  is   at  S,  equals  th«  above  sidereal  time  plus 
the  further  increase  in   right  ascension  during  the  meantime 
period    between  the   observer's   local    mean  noon    and  the  ob- 
server's   local    mean   time    of     Observation)*)*  local  hour  onqleMB 

Sidereal   time  gains  on  mean  time  9.8565  seconds  in  one 
mean  time    hour.  Observers   local  mean  time  differs  from 
observer's   standard  time  b>j  difference  in  longitude  between 
the  standard  and  the  observer's  meridian   divided   by    IS;  it 
is  earlier  than  standard  time  when  the  observer  is  west 
ot  the  standard    meridian. 

The  hour  angle  of  Polaris  eguals  observer's  sidereal  time 
m'mus    the    right  ascension    of    Polaris. 

The  ai-irnwth    of    polaris  at  S.    is    fownd    by  solving  the 
spherical   triangle    PZS,    for    the  angle    b   at  Z-. 


l"9 


Increase  >n   ngkr  ascension  in  the 
period   between   Greenwich  mean 
noon   and    the   local    mean  time    of 
observation   equals  *  n.« **•».» «>S  ••  •    h   \, 

Sidereal    time    when   Polaris    is  at  5,"  '0   ': 


ascension    of    Polaris    <vhen 

it  S, 

Hour    Angle    of     Polaris    at  5,  V" 

t -    156*    H' 
Declination     of    P«lqn»    ot  S,  +-88*91 


log  cos   L  *    9.  8-)7t8l 
loq  tan  5  =    1.701  2fcfe 
1.59854-1 


log    sin   U*    9.1  >  " 

t  oo,   cos.  t  »    J_J!  — 
9.fc,»i 

-  0.4  SO 


tan     b 


5  — 


co»t 


-       0.4-4-3  0 
4.  o .  I  Z  O  7 

toa    tint    «  9   84-01^5 
,.  .  -.     ^ 

log  4-o.'l8» 

log    tan  b  a 

b*  o"   sr  ig 


When   t  .*    Smaller    than     I8O*    Polaris   Is    west  of  the  meridian) 
when    areoter  than     i6O*.    Polaris    is  east  of  the  meridian- 


we»f    of    nort4i 
az-imuth     of    Poland    i» 
179"    OO1    41" 
.»».   8"   1"    S* 


Elem.    ofSurv.    1A  A-  3ir;r_Q'-nc,   II  Page   15 

V 

ie  greatest  near  the   horizon  and  d^ro.tsis  t-jF-ard  tha  zenith;  the 
correction  for  refraction  in  altitude  rili  a? ways   be   less  at  uoper 
culmination  (when  the  star's  observed  altitude   is  greatest)  and 
greater  at   lower  culmination  (when  the  observed  altitude  is  least). 
The  transit  used  in  this  work  should  be   equipped  with  a  full  ver- 
tical circle  and  the   angle  read  both   in  normal  and  inverted  .position 
of  telescope  to  eliminate  graduation  error.      The  mean  of  these  twp 
readings  is  to  be  taken  as  the  observed  altitude.     This  with  the 
corrections  for  polar  distance  and  refraction  give  the  latitude  ae 
the  net  result. 

References 

Breed  &  Hosmer,   pp.    212  -   220,  Vol.    I. 
Tracy,   pp.    354  -  360 
Raymond,  pp.    89  •  93 
Johnson,   pp.   30-36 

As  exercises  in  connection  with  this  assignment  it  is  recom- 
mended that  you  make  such  observationa  as  the  means  at  your  command 
permit.      You  may  study  the  heavens  to  locate  Ursa  Major  and  Cassi- 
opeia and  especially  by  means  of  these  to   locate  the  North  Star. 

An  instructive  exercise  would  be  the  determination  of  the 
meridian  by  the  plumb-line  method,  which  is  possible  witho-ut  ex- 
pensive apparatus.  In  Addition  to  this  the  magnetic  declination 
may  also  be  determined,. 


of  Surv.  1A          Adf  igrtart-  11          Page  14 


Questions. 

1.  The  declination  of  Polaris  on  July  1,  1921  is 
88  52  '461,1  what  is  the  azimuth  of  the  star--  at  elongation  for 
latitude  37°31'  North? 

2.  Find  the  times  of  upper  and  lov:er  culmination  of 
Polaris  on  November  10,  1921. 


of  Surv.   1A 


•n-ssigninerri,   li 


Page  15 


1921 


July   1 
July  15 
Aug.    1 
Aug.    15 
Sept.    1 
Sept.    15 
Oct.    1 
Oct.    15 
Nov.    1 
Nov. . 15 
Dec.    1 
Dec .    15 


TABLE   I. 
AZH.IUTH  OF  POLARIS  AT  ELONGATION,    1921 


Latitude 


AZ  imuth 


Latitude 


Azimuth 


30° 

1°17.  '  2 

31° 

1  18.  1 

32° 

1  19.  0 

33° 

1  19.  8 

34° 

1  20.  7 

35° 

1  21.  7 

36° 

1  22.  8 

37° 

1  23.  8 

38° 

1  24.  9 

39° 

1  26.  1 

40° 

1  27.  3 

4tO°       1°27.  '3 

41° 

1 

28,  5 

42C 

1 

29.  9 

43° 

1 

31.  4 

44° 

1 

32.  9 

45° 

1 

34.  6 

46° 

1 

36.  3 

47° 

1 

38.  1 

48° 

1 

40.  0 

49° 

1 

42.  0 

50° 

1 

44.  1 

TABLE    II 


TIME  OF  CULMINATIONS  OF  POLARIS 
Meridian  of  Greenwich  -  Mean  lime   -  Civil  Date 


Upper  Culmination 

h 

m 

8 

6 

57 

33 

A.  ttg 

6 

02 

46 

II 

4 

56 

15 

II 

4 

01 

27 

II 

2 

54 

51 

11 

1 

59 

59 

II 

0 

57 

13 

II 

0 

02 

14 

It 

10 

51 

28 

P.'id. 

9 

56 

21 

H 

8 

53 

19 

n 

7 

58 

05 

n 

Lower  Culmination 


h 

m 

s 

6 

55 

43 

P.M. 

6 

00 

56 

n 

4 

54 

25 

it 

3 

59 

37 

n 

2 

53 

01 

ti 

1 

58 

09 

ir 

0 

55 

23 

II 

0 

00 

24 

II 

10 

53 

18 

A.M. 

9 

58 

11 

it 

8 

55 

09 

n 

7 

59 

55 

M 

Difference  for   one  day:     3.7  minutes 


UNIVERSITY  OF  CALIFORNIA  EXTENSION   DIVISION 
CORRESPONDENCE  COURSES   IN  ENGINEERING  SUBJECTS 

Course   1A  Eleraents   of  Surveying 

Assignment  12 

SOLAH  OBSERVE  IONS   -   SOLAR   INSTRUMENT 

FOREWORD : 

This  assignment  v/ill  first   deal  with  the  necessary  astronom- 
ical phenomena  preliminary  to  methods  of  solar  observations  for 
meridian,    latitude,  and  time;   following  these  will   be   taken  up 
the  solar  attachment  and  its  use  in  solution  of  the  spherical  tri- 
angle for  determining  the   observer's  meridian;   and  finally,  the 
methods   of  direct  observations   on  the   sun  for  azimuth,    latitude, 
and  time. 

(104)   THE   SUN  AND  ITS  MOTIONS   IN   THE  HEAVENS 

in 
In  its  motions  the  celestial  sphere  the  sun  passes  through 

certain  unique  positions  aid  appears  to  an  observer  upon   the  earth 
to  traverse  a   somewhat  peculiar  path,   changing  in  its  equatorial 
distances,    its  time   of  rising;,  of  culmination  (or  transit  over 
any  meridian),   and  of  setting. 

The  cause   of  these   seemingly  irregular  movements   is  due  to 
the  fact  that   the  earth's  axis   is   inclined   at  an  angle  (23°27(   nearly) 
to  the  ecliptic  or  the   plane  of  the   path  in  whioh  the  earth  re- 
volves around  the   sun.     While  the  earth  in   its  diurual  rotation 
and  annual  revolution   is   passing  through  these  two  cycles   of 
change,  the   observer  upon  the  earth's   surface   sees  the    sun  as  though 
it  were  moving  upon  the   celestial   sphere.      Hence   the   sun  appears  to 


El en.    of  Surv.  Assignment   12  Page  2 

rise  at  a  different  point  on  the  eastern  horizon,   set  at  a  different 
point   on  the  western  horizon,    and  pass  from  rising  to  setting  over 
a  slightly  different  path  each  day. 

Xhe  explanation  is  probably  better  made   by  saying  that   the 
plane   of  the   ecliptic  and  the  plane   of  the   earth's   equator  are   in- 
clined to  each  other  by  the  angle   of  23°27'    (nearly).      Since  these 
planes   are   so   inclined  they  intersect   each  other  and  the  two  points 
upon  the  equator   (celestial   equator)   cut  by  the   ecliptic  are  called 
the  equinoxes,   because  when  the  earth  is  at  these  points,  the  days 
snd  nights  are  equal,  the  sun  rising  at  6  a..K.    and  setting  at  6  p.m. 
The  vernal  equinox  is  the   name  given  to  the  one  which  takes  place 
about  the  21st   of  March;  while  the  autumnal  equinox  occurs  about 
the   22nd  of  September.      Twice   a  year  the   sun  seems  to  reach  a  most 
northerly  and  most  southerly  point  in  its  course,  and  these  are 
designated  the  summer  solstice   (June  21st)   and  the  winter  solstice 
(December   22nd)    respectively. 

So  in  March  the  sun  appears  on  tine  equator,   and  in  June 
about   23°27'   northward,  the  change  being   sloxv,    from  day  to  day. 
The  angular  distance  measured  upon  the  great  circle  (a  meridian 
circle)   passing  through  the   sun  and  reckoned  from  the  equator,   is 
called  the   sun's  declination.      The   declination  may  be  either  north 
(+)    or  south  (-),    its  magnitude  varying  from  0  to  23°27'.     From 
June   to  September   its  north  declination  is  decreasing,   reaching  0° 
at   September   22nd;  then  changing  to  south  declination  it  increases 
until  Dec.    22nd.;   and  finally  decreases   in  south  declination  until 
it  again  reaches  the  equator  at  the  time  of  the   vernal  equinox. 


Elem.    of   Surv.    1A  Assignment    12  Page  3 

The  complement   of  the  declination  is  the  polar  distance; 
90°  -  d  =  P.D.    is  the   simple  equation  expressing  this  relation, 
and,    as  the  declination  is  positive   (-*-)  when  north  and  negative 
(-)  when   south,    the  P.D.    varies  between  90C   -  23°27'    and  90°  -f 
23°27',    i.    e.   between  66°33!   and  113°27'. 

Ihe  sun's  position  is  also  determined  by   its  altitude  above 
the   observer's  horizon,    or  rather  the  complement   of  the  altitude 
(90°  -  altitude)  which  is  the   zenith  distance. 

The  azimuth  of  the  sun  is   the  arc   on  the  horizon  measured 
between  the  meridian  and  the  vertical  circle  through  the  sun.      Reck- 
oned from  the  south  point  of  the  horizon,   generally,  the  azimuth 
is   180°  greater  than  when  taken  from  the  north  point. 

The   right  ascension  is   the   sun's  distance   in  arc  from  the 
vernal   equinox  measured  eastward  upon  the  celestial  equator.     An- 
other co-ordinate  called  hour   angle   is  the  arc  of  the  equator 
measured  westward  from  the  meridian  to  the  hour  circle  through 
the   sun.      These  two  arcs  are  conveniently  expressed  in  time  units, 
hours,  minutes   and  seconds,    out  may  readily  be   reduced  tc  degrees, 
minutes,   and  seconds   (°,    ',    ")  as   occasion  requires.     Kight  ascen- 
sion is  the  hour  angle   reckoned  from  the   vernal   equinox. 

From  the  foregoing  considerations  we  have  three  systems  of 
c o-ordi nates ,    as  follows: 

(1)  The  Horizon  system  employing  altitude  and  azimuth;    (2) 
the  Equatorial  system,   which  makes  use   of   the   declination  and  hour 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 
CORRESPONDENCE  COURSES  IN  ENGINEERING  SUBJECTS 

PLANE  SURVEYING 

•   COURSE  X-lA 


PLATE  IX 

MOUNTAIN  AND  MINING  TRANSIT 

FITTED  WITH 
SMITH  SOLAR  ATTACHMENT 


PLATE  VIII 

ENGINEERS  '  TRANSIT  PITTED  WITH 
SAEGMULLER  SOLAR  ATTACHMENT 


El  em.    of  Surv.    IA 


Assignment  12 
THE;   CI.LESIIAL  SKffJxE 


Page  4 


0,   the  earth  at  center  of  sphere 
ES1NN  Plane  of  aorizon 
SQZPN     Meridian   of  observer 
EQW     Plane  of  equator 
MR  I     Sun's  path 

Angular  distance  of  sun  from 
equator  at  any  time  is 
sun's  declination,  which 
is   continually  changing. 

Alt.      Sun's  altitude 
Sun  -  Z     Zenith  distance 
PN  =  QZ     Latitude 
ZP  =  90°  -  QZ     Go-Latitude 

Zenith  distance  is     the  com- 
plement of  the  altitude, 
i.e. ,   90°  -  altT~ 


Co-Latitude  complement  of   latitude  -   i.e.,    90°  -   Lat. 

Polar   distance  complement   of  declination    -   i.e.    90°  -  Declination. 
And,    since  the   declination  may  be  either  +,  when  north,   or  -, 
when   south,   this  arc    (Polar  Dist.)  will  vary  between  66°33'   and 
113°27'. 

Arc  NX,   the  measure  of  angle,    Sun-ZP,    is  the  sun's   azimuth. 

Arc   of  equator  QY,   measure   of  ang.le   Sun-PZ ,    is   the   sun's  hour-angle. 

Refraction  Corrections  for  Altitude 


Alt. 

Ref. 

Alt. 

Ref. 

Alt. 

Ref. 

10° 

5  '16" 

18° 

2'  56" 

30° 

1'40" 

11 

4  43 

19 

2  46 

35 

1  22 

12 

4  24 

20 

2  37 

40 

1  09 

13 

4  04 

21 

2  29 

45 

0  58 

14 

3  47 

22 

2  22 

50 

0  48 

15 

3  32 

23 

2  IE 

GO 

0  33 

16 

3  18 

24 

2  09 

70 

0  21 

17 

3  07 

25 

2  03 

80 

0  10 

Elera.  of  Surv.  IA          Assignment  12  Page  5 

angle  (or  Right  Ascension);  and  (3)  the  Terrestrial  system,  using 
the  latitude  and  the  longitude,  which  define  the  observer's  po- 
sition upon  the  earth.   This  last  is  the  one  which  must  be  deter- 
mined by  the  surveyor,  and  hence  all  observations  of  an  astronomi- 
cal nature  follow  this  system. 

By  reference  to  the  diagram  (Fig.  32)  showing  the  celestial 
sphere,  with  the  accompanying  explanations,  the  foregoing  definitions 
will  be  made  more  intelligible. 

)5)  DETERMINATION  OF  MERIDIAN 

The  solar  attachment  must  be  carefully  adjusted  (see  Assign- 
ment XIV  for  detailed  directions  for  these  adjustments) . 

Having  determined  the  declination  settings  for  the  times 
of  observation,  bring  the  solar  telescope  and  the  transit  telescope 
into  the  same  vertical  plane  by  sighting  both  upon  the  same  point. 

(a)  Set  off  the  declination  for  the  time  of  observaxion  on 
the  vertical  circle  with  transit  telescope  pointing  southward;  if 
the  declination  is  north,  depress  the  telescope;  if  south,  elevate 

it. 

(b)  Clamp  the  transit  telescope   in  this  position,  and  level 
the    solar  telescope;   the   solar  is  now  in  the  horizon  and  the   angle 
between  the   solar  and  the  transit  telescopes   is   that   of  the   sun's 
declination.      Xhe  r.ngle  formed  by  the  polar  axis   and  the   solar 
telescope  will   be   the    sun's   polar   distance   (90°  ±  declination). 

(c)  Unclamp  the  horizontal  axis   of  th*    transit  telescope 


Elera.    of  Surv.    IA  Assigiiaent   12  Page   6 

and  set  off  the  co-latitude   of  the  observer's  position  on  the  ver- 
tical circle.      The  latitude  may  be  taken  from  a  map  or  may  better 
be  determined  by  a  previous  observation  for  latitude.      The  polar 
axis  now  points  to  the  Pole. 

(d)  With  the    lower  motion  of  the  transit  and  that  of  the 
solar  undamped,    (if  in  the  northern  hemisphere,   pointing  in  a 
southerly  direction)  the  two  telescopes  may  now  be  turned,   each 
about  its  vertical  axis  by  means  of  the  tangent  screws,  until  the 
sun  can  be  followed  in   its  path,    its   iraag^e  falling  symmetrically 
upon  the  field  of  the    solar,   thus: 


As  the  sun  changes    less  than   one  minute   of  arc  per  hour,   the 
time   is  ample  for  making  the  setting  of  the  sun's   image  and  may   be 

<w- 

followed  in  this  phase  for  several  minutes. 

f 

The  position  of  the  combined  instrument  is  now  as  follows: 
The  Polar  axis  points  to  the  Pole;  the  solar  telescope  to  the  sun; 
the  transit  telescope  is  in  the  plane  of  the  meridian,  and  the 
triangle,  Sun-ZP,  has  been  mechanically  solved. 

3et  r-  stance  beneath  the  transit  and  a  small  tack  exactly  at 
a  point  A,  defined  by  the  plumb  bob.  Depress  the  traasit  telescope 
and  at  a  point  B,  600  feet  or  more  distant,  set  another  stake  with 
a  tack  center.   Plunge  the  telescope  and  at  several  hundred  feet 
to  rear  set  still  another  stake,  C,  with  tack  center^  if  the  line 
of  collimation  of  the t ransit  telescope  is  at  right  angles  to  the 
horizontal  axis,  the  line  BAG  will  be  a  straight  line  coinciding,  with 
a  meridian  on  the  earth.   From  this  line  the  true  azimuth  of  any  line 
may  now  be  determined. 


Elan,  of  Surv.  1A         Assignment  12  Page  7 

Also  observe  the  position  of  the  magnetic  needle  for  mag- 
netic declination* 

Should  it  be  desired  to  determine  the  true  azimuth  of  any 
line  passing  through  the  point  occupied  by  the  transit,  read  the 
limb  and  then  open  the  upper  motion,  sight  upon  a  point  in  the 
line,  and  again  read  the  limb.   Or,  more  conveniently,  if  the  A 
vernier  is  set  to  zero  on  the  limb,  then  the  azimuth  angle  may  be 
read  directly.   Should  it  be  desired  to  determine  the  azimuth 
angle  accurately,  employ  the  method  of  repetition,  using  the  points 
B  (to  the  south  for  south  azimuths)  and  C  (to  the  north  for  north 
azimuths)  as  points  of  reference. 

(106)  LATITUDE,  OBSERVATION 

The  meridian  having  been  laid  out,  the  transit  may  be  easily 
brought  again  into  the  same  meridional  position  and  the  altitude  of 
the  sun  taken  at  apparent  noon  (i.e.  when  the  sun  is  on  them«rid- 
ian).   Then  having  computed  the  declination  for  the  day  and  hour 
(apparent  noon  of  the  date  of  observation)  you  may  compute  the 
latitude.   The  following  formula  is  applicable: 

Lat.  =  90°  -  h  ±  d,  in  which  h  is  the  altitude  of  the  sun's 
centex",  and  _d  is  the  sun's  declination.   The  value  of  h  must  be 
corrected  for  the  semi-diameter  of  the  sun  (approximately  16') 
when  observing  for  altitude  upon  either  upper  or  lower  limb,  sub- 
tracting this  correction  from  h  if  the  upper  limb  is  used,  adding 
the  correction  to  h  if  the  lower  limb  is  used.  Also  d  must  be  cor- 
rected for  refraction,  added  when  sun  is  north  and  subtracted  whea 


Elem.  of  Surv.  1A          Assignment  12  Page  8 

sun  is  south  of  equator.   (This  applies  for  observations  made  in 
the  northern  hemisphere.)  Furthermore  the  altitude  of  the  sun's 
center  should  oe  corrected  for  cefraction  in  altitude;  or  this  last 
correction  may  be  applied  to  the  computed  latitude.  As  refraction 
always  causes  the  apparent  altitude  to  be  greater  than  the  true 
altitude,  the  sun's  apparent  polar  distance  will  always  be  less 
than  the  true  polar  distance. 

r)   DIRECT  OBSERVATION  Ow  SUN  FOR  MERIDIAN 

Compute  the  declination  at  time  of  observation  and  from  this 
obtain  the  polar  distance,  which  is  equal  to  90°  -  d  (d  is  -*•  at 
north  declination,  -  at  south  declination^. 

Observe  the  sun  for  altitude,  making  correction  for  semi- 
diameter  and  for  refraction  in  altitude,  and  from  this  obtain  the 
zenith  distance,  which  is  equal  to  90°  -  alt. 

The  latitude  (from  a  good  map  or  previous  observation  for 
latitude)- subtracted  from  90°  gives  the  co-latitude  1,  (co-lat.  = 
90°  -  lat.) 

Let  S  =  1/2  (P.D.  +  co-lat.  +  Z.D.),  then 


cos 


1/3  sun's  azimuth  =  j/8in  f    Si"  <S"P'D'  > 

]/  sin  co-lat.  •  sin  Z.D. 


which  lends  itself  readily  to  logarithmic  computation;  thus  log  cos  1/2 «A  - 
-r-(log  ain  8  "''log  sin  (S-P.D. )  •*•  colog  sin  co-lat.  -f  colog  sin  Z.t. ) 

(103)  TO  OBSERVE  TIME  iwirh  SOLAR 

}.iake  the  observation  for  meridian  ae  above  directed.   Note 
the  time  on  watch  at  the  instant  that  the  sun  is  centered  in  field 


d" 


Breed  &  Hosmer  Vol.  I,  pages  63  -  7Q 


Elein.  of  Surv.  1A          Assignment  12  Page  9 

of  sclar  and  clamp  the  solar  telescope. 

Set  the  forward  stake  with  a  tack  center  by  pointing  the 
transit  telescope  without  changing  the  solar.   Return  the  transit 
telescope  to  a  horizontal  by  means  of  its  level,  and  clamp  the 
notion.   The  polar  axis  now  points  to  the  zenith.  By  inclining 
the  solar  telescope  set  a  stake  with  a  tack  center  bisected  by  the 
vertical  cross-hair  at  the  middle  of  the  solar  field.   This  stake 
should  be  200  feet  or  more  distant. 

Then  by  a  use  of  the  transit  limb,  measure  the  angle  bet'.veen 
the  meridian  previously  set  and  the  last  mark.   This  is  the  hour 
angle  or  Right  Ascension  in  °,  ',  ",  which  must  be  reduced  to  time 
units,  hrs. ,  rains.,  sees. 

Compare  the  time  thus  obtained  with  the  watch  and  set  the 
latter  fast  or  slow  as  required;  or,  if  it  is  not  desirable  to 
change  the  watch,  this  difference  may  be  noted  as  a  correction  for 
all  time  observations.   If  the  watch  time  is  the  so-called  "standard" 
time,  this  must  be  changed  to  local  mean  time  before  comparison  is 
made. 

QUESTIONS: 

1.  (a)  Change  14*  37'  42"  to  time  measure. 
(b)  Change  3h  40m  15s  to  arc  measure. 

2.  An  observer  in  longitude  124°  07'  58"  notes  the  time  of 
his  watch  is  8:43-1/4  A.M.,  Standard  Time.   Required:   The  Mean 
local  time  of  the  observation. 

REFERENCES ; 

Tracy  Appendix  I,  page  620 

Raymond  Pages  116  -  126 

Johnson  Pages  99  -  102. 

Breed  &  Hosmer  Vol.  I,  pages  63  -  70 


iY  OF  CALIFORNIA  bX'i'LiiSLJK   II  VISION 

.NCF.  comsbs  iw  ENGINEERING  SUBJECTS 


Course   1A  Elements   of  Surveying  Swafford 

Assignment   13 

ADJUSTMENT   OF  INSTRUMENTS 

FOREWOHD : 

This  assignment  will  deal  with  the  usual  adjustments  of 
surveying  instruments,  special  attention  being  given  to  those  made 
in  the  field.   The  methods  of  detecting  instrumental  errors  of  the 
more  serious  kinds  -  auch  as  would  require  the  skill  and  appliances 
of  the  instrument  maker  -  and  of  correcting  them,  will  also  be 
pointed  out.   As  references  will  be  made  to  the  various  sections 
of  this  assignment  in  the  matter  of  instrumental  adjustments,  a 
simple  system  of  numbering  the  several  paragraphs  has  been  carried 
out.   The  scheme  will  be  quite  evident  after  a  few  moments  of  study. 
09)  (A)  SPIRIT  LEVEL 

(1)  Adjustment  depends  upon  a  principle  called  reversion. 
If  the  bubble-tube  is  placed  longitudinally  parallel  to  a  truly 
horizontal  line  and  the  position  of  the  bubble  noted,  the  bubble 

should  have  the  same  position  if  the  bubole-tube  is  reversed 
through  180°.   In  Figure  33  the  bubble-tube .has  the  position  MN 

mr~ 


Figure  33  '?  i.par,-,    34 

on  the   horizontal   line  ^B j   the  bubble   is  at  0,    the  middle   of  the 

tube.      In  Fig.    34  the    line  AB   remains   unchanged,    but  the    DubDle-tuoe 
is   reversed  through   180°  to  the  position  HH;   the  bubble   should  now 


Elem.    of  Surv.    IA  Assignment   13  Page  2 

be   in  the   same  relative  position  in  the  tube,    i.e.    at  0.      If  the 
bubble-tube  were   revolved  upon  a.  horizontal  plane  through  360°, 
the  relative  position  of  the   bubble  would  not   change. 

(2)  Experiment  may  be  made  by  the    student  with  a  carpenter's 

common   level,   as  follows: 

piece  of 
Joint  up  the  edge   of  a/^board  about  6   inches  wide  by  3  feet 

long,    so  as  to  have  a  true,    fiducial  edge.     Clamp  lightly  in  a 
bench-vise  and,   by  placing  the   level  upon  it,  bring  it  to  a  hori- 
zontal position  in  the  vise.      Reverse  the  level.      Does  the  bubble 
stand  at  the  middle  of  the  tube   as  before?      If  not,  what  must  be 
done  with  the  board  in  the  vise  to  cause  the  bubble  to  return  to 
the  mid-position?     Do  this,    and  again  reverse  the   level  to  the 
first  position.     What  do  you  notice  regarding  the    bubble  now? 
Alter  the   slope  of  the  board  in  the  vise  so  as  to  cause  the  bubble 
to  approach  half-way  to  mid-position,  and  reverse  the  level.      You 
will  now  note  that  the  bubble  will  occupy  the   same  relative  position 
in  the  tube  no  matter  which  direction  the   level  has  with  respect  to 
the  straight  edge.      Hence  : 

(3)  To  adjust  a  carpenter's   level. 

Use  a  straight  edge  as  in  the  above  experiment;   level  up 
carefully;  reverse  the    level  through  180°;  bring  the  bubble  half- 
way to  center  by  tilting  the    straight-edge  in  the  vise;  correct 
the  setting  of  the  bubble-tube   in  the  level-block.      In  the  ad- 
justable  level,   a  screv:  acting  at   one  end  of  the  brass  protecting 
plate  enables   one  to  raise   or  lower  that    end  of  the    bubble-tube. 


Elem.  of  Surv.  1A          Assignment  13  Page  3 

Some  levels  require  the  protecting  plate  to  be  removed,  revealing 
the  adjusting  screw  beneath.   Still  other  levels,  those  of  the 
cheaper  kind,  have  the  tube  imbedded  in  cement  (plaster  of  Paris) 
and  are  not  adjustable. 

The  principle  of  reversion  ijs  applied  jln  making  level  ad- 
justments _on  all  surveying  instruments  and  will  frequently  be  re- 
ferred to  in  what  follows  respecting  adjustments.   (See  A-l,  1st 
adjustment. ) 

(110)  (B)  ADJUSTMENTS  OF  THE  SUKVEYOR'S  COMPASS 

(a)  Ihe  needle  in  the  compass  should  be  (1)  Balanced  on  the  pivot, 

(2)  straight,  that  is  ir.  the  same  vertical  plane  through  the  pivot, 

(3)  well-magnetized  so  that  it  responds  promptly  to  the  earth's 
action. 

(1)  To  balance  the  needle,  level  the  plate  carefully  and 
observe  whether  the  ends  of  the  needle  are  equally  disposed  with 
respect  to  the  graduated  circle;  if  not,   move  the  coil  of  fine 
wire  on  the  south  end  so  that  the  needle  balances.   To  do  this  it 
is  necessary  to  remove  the  glass  cover  and  take  the  needle  from 
the  box. 

(2)  To  straighten  the  needle.  By  observing  both  ends  of 
the  needle  it  is  possible  to  determine,  first,  if  the  needle  is 
straight;  second,  if  the  pivot  on  which  it  turns  is  in  the  line 
of  sight  of  the  two  standards.   If  the  pivot  is  at  the  center  of 
the  graduated  circle,  and  the  needle  straight  the  readings  of  the 
opposite  ends  will  -show  a  constant  difference  of  180°.   If  the 


Elea.  of  Surv.  LA.          Assignment  13  Page  4 

needle  is  concave  to  the  right,  the  right  hand  segment  of  the  circle 
will  be  less  than  180°  and  consequently  the  left  hand  segment 
greater  than  180°  for  every  position  of  the  needle.   In  such  case 
remove  the  needle  and  support  it  near  its  ends,  laying  it  upon 
the  concave  side,  and  press  it  gently  to  make  it  straight,   •test 
it  frequently  by  returning  it  to  the  pivot  and  observing  if  it  is 
straight.   If  the  needle  is  straight  and  the  pivot  is  not  at  the 
center  of  the  graduated  circle,  the  needle  reading  of  its  two  ends 
will  differ  by  exactly  180°  in  only  two  positions,  which  will  be 
themselves  180°  apart.  All  other  readings  than  those  just  men- 
tioned will  differ  from  180°,  one  .segment  being  less  than  180°, 
the  other  greater  than  180°.   To  adjust  the  pivot  in  such  case, 
determine  the  line  of  no  difference,  remove  the  needle  and  care- 
fully press  the  pivot  in  the  direction  of  this  line  forward  or  ' 
backward  so  that  the  needle  will  give  readings  that  differ  by  180°, 
when  at  right  angles  to  the  line  of  no  deviation.  The  pivot  having 
been  adjusted  and  the  needle  straightened,  adjustment  (3)  is  made. 

(3)  To  Magnetize  the  Needle 

Remove  the  needle  from  the  box  and  support  it  throughout 
its  length;  stroke  it  with  a  bar  or  horse-shoe  magnet,  applying 
the  north  end  of  the  magnet  to  the  south  end  of  the  needle,  or  the 
south  end  of  the  magnet  to  the  north  end  of  the  needle .   The  needle 
can  also  be  quickly  magnetized  by  bringing  it  into  contact  with  the 
poles  of  a  dynamo  or  motor  while  current  is  passing  through  them. 
Of  course  these  must  be  of  the  direct  current  (D.C.)  type,  and  the 


Elem.  of  Surv.  1&,         Assignment  13  Page  5 

needle  placed  in  position  with  south  end  at  •*•  pole  and  north  end 
at  -  pole  of  the  motor  or  generator.   If  a  mistake  has  been  made 
at  first  trial,  the  error  may  be  corrected  by  reversing  the  needle 
in  a  second  trial  and  allowing  it  to  remain  in  contact  long  enough 
to  remedy  the  fault.   The  following  conditions  should  now  obtain; 

1)  The  standards  should  oe  vertical  vidhen  the  compass  plate  is 
horizontal. 

2)  The  line  of  sight  should  lie  in  a  plane  passing  through  the 
slits  in  the  two  standards  and  including  the  central  pivot  on  which 
the  needle  swings  and  the  exact  north  and  south  points  of  the  grad- 
uated plate.   These  matters  require  the  attention  of  the  maker. 

11)  (C)  DUMPY  LEVEL 

(1)  T_o  adjust  the    horizontal   cross-hair  to  true  horizontality, 
sight  on  some  well  defined  point  at  a  distance   of  about  50  feet, 
setting  one  end   of  the  horizontal  cross-hair  upon  it.      Turn  the 
telescope  about  the  vertical    axis  and  if  the  point  remains  on  the 
cross-hair,  the   latter  is  horizontal;   if  not,   it  requires  adjusting. 
To  do  this,    loosen  the  four  capstan-head  screws  that  hold  the  cross- 
hair reticule,  turn  the   latter  to  right   or  left  as   the  case  may  be 
until  the  distant  point  is  made  to  "thread"  the  horizontal  cross- 
heir  throughout   its   length.      This  adjustment   is  then  complete. 

(See  Print  A-i,   Preliminary.) 

(2)  To  coMirr-.ate  the  telescope,   unscrew  the   plate  which  holds 
the  pinion  operating  the   object   tube.      This  will  permit  the  tube 
containing  the   optical  parts  to   be   rotated,      how  sight  upon  a 


Elem.    of  Surv.    1A 


Assignment  13 


Page  6 


distant  point,    rotate  the  tube,   and  ooserve   the  position  of  point 
of  intersection  of  crose-hair  with  respect  to  the  chosen  point. 
If  they  remain  in  coincidence  throughout   a  complete  revolution  of 
the   optical  tube,  the   line   of  collimation  is  correct.      If  they  do 
not,    loosen  the   opposite  pair   of  screws  holding  the  cross-hair 
reticule  and  tighten  first  the  one  that  dra?;s  the  reticule  toward 
a  correct  position;   repeat  with  the  other  pair  of  opposite  screws 
to  bring  the  cross-hairs  into  position  in  the  second  direction. 
"When  finally  the    point  and  cross-hairs  are  coincident  tighten  the 
reticule   screws,    being  careful  not  to   overstrain  them.      The  focus 
of  the   objective  now  falls  upon  the  optical  axis   of  the   telescope, 
and  at  the  point  of  intersection  of  the  cross-haire;   i.e.,  the 
instrument   is  collimated.      In   some  levels  this  adjustment  cannot 
be  made. 

(3)  Tc>  make  the  axis  of_  ou  bole-tube  parallel  with  the   line 
of  collimation,   set  up  the   level  L  at  a  place  where  two  points  A 

and  B   about   300  or  400  feet  apart  and  at   nearly  equal  distances 

held 
from  the   instrument  can  conveniently  be  sighted.      Read  a  rodA.at 

each  point   in  turn  and  record 

Rod  Reading     at  A       4.527 
11          "  "     B        5.213 

A  -  B        1.314       True  Diff.    in  Elevation 
Instrument  at   LJ. 

Remove   level  to  position  L.^,   ten  feet   oeyond  3  and  approxi- 
mately  in   line  with  A  and  B.      head  the  rod  set  upon  A  md  B   as 


ADJUSTMENTS   OF  THE  DUMPY  LEVEL 


PRELIMINARY 

Focus  eye  piece  on  cross-hairy  ,  and  make  horizontal  cross  \ 
per  pen  a  '/cu/ar  to  ax  15   of  rotation  of  instrument. 


FIRST  ADJUSTMENT >•  Bubble 

To   make  axis  of  bubble-tube  perpendicular  to   ax/5  of 
rotation  ,  or  vertical  axis,  of  instrument. 


FI6.  1 


Axis  of  bubble  -tube 


Horizontal  line 


Level  instrument  carefully 


Turn  instrument  end  for  end  on  OKI 
of  rotation  (this  reverses  bubble--iiet 

The  apparent  error  (?e)  is  twice  ht 
true  error  (a) 


Bring  bubble  halfvyay  back  to  cente: 
by  means  of  adjusting  screws  af  t1 
of  bubble- tube 


II  | 


Horizontal   line 


VT 


Center  bubble  by  means  of  leveling  scrt  5 


FIG  IV 


C.T  YVttKC"  _^ 


ADJUSTMENT  .--  Line  of  sight 

To  make  l/ne  (f  sight  parallel  to  axis  of  bubble-tube , 

Direct  or  'PecfAajustment " 


Fie.v 


6.103  c. 
6019 


'"Correct  position  of  line  of  sight    (Horizontal    line) 


First  position  of  line  of  si 


3H 
-Any  distort 

say  30 fe 


Set  instrument  up,  in  line  with  and  half-way  between  two 
hubs,  B  and  C,   which  are  from  ?00  to  400  feet  apart.  Pead 
rod  on  each  hub.  As  lengths  of  B.5.  and '  f:S  are  equal ,  errors 
of  adjustment  are  eliminated  and  the  true  difference    in 
elevations   of  B  and  C  b  obtained   by  subtracting    the   rod 
readings. 

Now  set  up  again  near  either  hub,  say  at  D,  and  again 
take  rod  readings  on  B  and  C.    If  the  instrument  is   in 
adjustment   the  difference  in  elevation    of  B  and  Cf  as  obtained 
from  these  last  two  readings ,  will  agree  with  the  true 
difference   in  elevations.    If  the  instrument  is  not  in 
adjustment   determine    the    amount   of  error. 

TO  COPPECT  EPPOP 

Dumpy  level :-     With  bubble  centered ,  bring  line    of  sight 
correct  rod  reading    at  B  by  means   of  the    capstan  screws 
that  move    the    cross -hair  ring, 

Wye  level  ••-    By   means   of  the   I  eve  I  ing -screws  bring 


line  of  5/ght  to  correct  reading  at  B,  then  bring  bubble 
of  tube  by  turning  the    capstan    nufe  at  the  end  of 
bubble-  tube. 

Form  of  Note? 


Instrument  at 
A 


D 


Pod  at          heading 
d  2.938  ' 

C  0,972 

1,966    True  difference  in  e/evation. 


C  4,127 

d  e.ofe 

1 .892  Fabe  difference  in  elevation. 

Thb  b  less  than  the  true  difference   in  e/evation,  therefore 
the  line  of  sight  is  inclined  downwards.  (The  hub  at  0  being 
lower  than  the  hub  at  C) 

True  difference  in  elevation  1,966 
fly/se  difference  in  elevation  1,892 
Error  in  distance  L  0,074  feet 

Total  error  in  line  of  sight  in  the    distance   Dd 
,  &4 +30)  x  0,074  =  0.084  feet 

Target  setting  at  5  to  give  horizontal  line    is    6, 019 
+0.084  =  6,103* 


Note:-   To  determine    whether    the    correction  is  to  he 
or  subtracted  draw  a  figure   in  your  field  book   representing 
the  specific     case    In  hand.      5how  clearly   relative    elevation" 
of  hubs. 

*  For  exact  adjustment  this  rod  reading  should  be  corrected  by 
adding  the  effect  of  curvature  and  refraction   which,  in  this  i 
Is  approximately   0,001  feet.      The  target  setting  at  B  would  then 
be  6.104 


El em.    of  Surv.    1A  Assignment  13  Page  7 

before;  we  shall  now  have,  suppose 

Rod  Reading  at  A  7.235 

"     B  5.685 

A  -  B  1.552     False  difference   in  Elevation 
Instrument  at  L,,. 

Subtract  the  true  difference  in  elevation  from  the  false 

difference  and  take  —is-,  of  this  difference. 

40 

False  Difference   in  Elevation     1.552 
True  "  "          "  1.314 

0.238 

which  multiplied  by  — ~—  =  0.244.      This   quantity  deducted   from 
last  rod-reading  at  A  (7. £35  -  0.244  =  6.991)  will  be  the  target 
setting  for  A,    level  at   Lg,    in  order  that  the   line   of  sight   (line 
of  collimation  prolonged}   may  be  horizontal.     With   the   target, 
therefore,    set  at  6.991  and  rod  held  on  A,   direct  the  telescope 
to  the  target  by  means  of  the  leveling  screws   of  the   instrument, 
and  while  it   is   in  this  position  raise  or    lower  the    level-tune  by 
means  of   the  adjusting  screws  at  one  end  of  the  tube  until  the 
buoble   is  exactly   in  the  middle  of  its  ran.      It   should  be  apparent 
now,   that  whenever  the   bubble   is   at   the  middle   of   its   tube,    the 
lime  oi   sight  will  be  truly  horizontal.      The  foregoing  is  called 
the    "Peg  Method"  of  adjusting  the   level  and   telescope,  and   should 
be  well  mastered  by  the  student,  as   the   same  routine   is  followed 
in  making  this  adjustment   in  case  of  the  Wye-level,    or  the   Transit, 

(See  A-3,    Second  Adjustment.) 
(  See  Fig.    A- 1-  ) 


Elem.  of  Surv.  1A          Assignment  1?  Page  6 

(112)  SETTING  UP  AND  PhLLIMINARY  ADJUSTMEHTS 

These  relate  to  instruments  in  general  and  are  supplemental 
to  the  directions  furnished  in  connection  with  other  assignments  of 
this  course. 

For  purposes  of  field  adjustment  the  instrument  should  be 
set  up  in  a  shaded  spot  on  reasonably  level  ground,  in  a  locality 
free  from  interference,  ef.rth  shakings  and  local  magnetic  attrac-- 
tions.   In  compass  adjustments  avoid  proximity  to  electric  lines 
or  pipes  buried  in  the  ground.   The  stretch  of  open  space  (different 
for  different  cases)  should  be  of  sufficient  extent  to  permit  all 
adjustments  to  be  completed  with  one  setting  of  the  instrument,  or, 
in  case  two  or  more  settings  are  required,  to  permit  them  to  be 
made  with  ease  and  facility,  so  as  to  secure  the  advantage  of 
freedom,  stability,  and  range. 

L13)  PRELIMINARY 

Plant  a  tripod  firmly,  spreading  the  legs  at  angle  of  about 
60°,  so  as  to  secure  a  broad  base  which  adds  to  stability.   Press 
the  shoes  well  into  the  earth,  which  should  be  solid  and  free  from 
loose  sand  or  marsh.  Bring  the  head  of  the  instrument  as  nearly 

level  as  possiole  in  the  foregoing  processes,  so  that  the  final 

up 
work  of  levelingAmay  be  done  with  ease  and  dispatch. 

Examine  clamp  screws,  pivots,  etc.,  to  see  that  all  parts 
are  free  to  turn  without  requiring  undue  force.   If  a  telescope  is 
a  part  of  the  instrument,  uncover  the  objective  and  eye-end,  and 
move  the  objective  tube  in  to  the  shortest  telescope  length,  direct 


Elein.    of  burv.    IA 


Assignment   13 


.Page  9 


it  toward  the   sk^ ,   away  from  the    sun,    and  observe  the  appearance 
of  the  cross-hairs,      fhese  should  stand  out  clear  and  sharply 
defined  -  even  the  particles  of  dust  invariably  present  should  be 
plainly  visible.      Sight  upon  sortie  well   defined  distant  object  and 

observe  for  parallax,    by  shifting  the  eye  first  to  one   side  of  the 

to 
eyepiece,   then/vthe  other  -  then  up  and  down  in  similar  way,  and 

note  if  the  cross-hairs  appear  to  move   over  the   field  of  view.      If 
they  do,   parallax  is  present,    and  must  be  removed  by  careful  ad- 
justment of  the  eyepiece.     Many  telescopes  have   a  set-screw  for 
clamping  the  eyepiece  when  in  adjustment.      The  eye-piece  should 
be  clamped  if  the   instrument  is  to  be  used  by  one  person,  as   in 

0 

that   case  the   eye-piece   setting  will  not  require   change. 

Next   level  up  the  plate   or  what  is  really  the  case,   bring 
tke  axis  of  the  instrument  into  verticality  by  means  of  the  level- 
ing screws  on  the  tripod  head.      This  important   step  should  be  done 

as   follows: 

Set  a   level  in  line  with  two 
diagonally   opposite  footscrews,  as  A 
and  B   in  the  adjoining  figure. (Fig.    35) 
Grasp  a  screw   between  thumb  and  fore- 
finger,   one   in  each  hand  and  proceed 
to  turn  both  in  or  put,   uniformly,    and 
observe  the  direction   in  trhich  the 


Fig.    35 


bubble  moves  -   it  will  alv.-ays  follow  the  right-hand,      finger  or 
the   left-hand  thumb  -  and  thus  bring  the    bubble  to  the  mid-point 


Elem.    of  Surv.    1A  Assignment  13  Page   10 

of  its  tube.      Next  set  the   level   over  the  other  pair  of  foot-screws 
and  proceed  as  before,      barring  possible  necessary  adjustment,   de- 
scription of  which  will  follow  these  preliminaries,  after  a  few 
trials  the   level   (or   levels)  will  be  &t  mid-point  for  all   positions. 
The   level-plate  will  then   oe  horizontal  and  the  vertical   axis  truly 
vertical. 

In  manipulating  these  foot    screws   it  may  happen  that  they 
"bind",    and  can   be  moved   only  with  increasing  difficulty;  this   is 
due  to  one  screw  traveling  faster  than  its  opposite.      The    "binding" 
will  be  removed  if  you  continue  to  turn  either   screw  in  a  right- 
hand  direction  (clockwise  when  viewing  the  bottom  of  the   screw); 
but   the  quickest  method  is  to  turn  both  screws  together  to  the 
right  (clockwise).      Sometimes  the    binding  of  one  pair  of   screws 
is  due  to  the  position  of  the   other  pair,  and  the   latter  should 
receive  attention.      In  no  event  permit  the   screws  to  bind  and  of 
all   things,  do  not  continue  to  turn  them  when  they   do  bind,   except 
in  the  manner  required  to  loosen  them.     All  screws  used  in  manip- 
ulating the   instrument  -  foot-screws,   clamp-screws,  tangent  screws, 
etc.    -  must  at  all  ti;aes  turn  easily  and  freely.     When  they  do  not, 
they  need  attention.      Do  not   oil  screws  or   bearing  parts.      Oil  will 
cause  grit  and  dust  to  adhere   to  such  surfaces  and  this   in  time 
will  cause  the  parts  to  wear  rapidly. 


Elem.  of  Sv»rv.  1A 


Assignment  13 


Page  11 


•*<__  —  •== 

>     -« 

is 

El 

m 


Figure  36 


•3 


Suppose  a  level-tube 
connected  cy  supports  s  s1  with 
the  line  AB  and  it  is  desired 
to  make  the  line  truly  horizon- 
tal. Adjust  the  line  so  that 
the  bubole  is  at  center  0;  re- 
verse to  position  180°  as  at  b, 
Figure  36,  by  revolving  about  C. 
The  buoDle  will  now  be  at  the 
high  point  j>;  but  by  shortening 
the  support  s1  the  tube  may  be 
brought  into  parallelism  with 
AB  as  at  £,  the  bubble  is  then 
at  ^,  midway  between  o  and  p. 
If  now  the  line  BA  is  tilted 
until  the  oubble  again  takes 
the  position  o,  as  in  d,  BA 
will  be  parallel  to  the  bubble- 
tube  and  in  a  horizontal  position 


the  axis  of  rotation,  C,  will  also  be  vertical  (a  plumb  line). 


REFEEENCES : 


Tracy 

Raymond 

Johnson 

Breed  &   Hosiner 


Pages   581  -  606 

63,   79,    108 
15,   63,    86,    102 
25,    56,   70,    89 


Elements  of  Surveying-lA 


Assignment  13 


Page 


QUESTIONS: 


1. 


The  lines  of  a  tape  survey  of  a 
field  are  noted  on  the  adjoining  figure. 
Compute  the  areas  in  acres. 


2.  3y  a  single  set  up  at  0  the  angles  about  (were  measured 
and  the  distances  to  M,  N,  P,  &  R  measured;  from  the  data  thus 
obtained  compute  the  area  of  the  field 


Angles 

MON  60° 

NOP  87° 

FOR  92° 

ROM  117° 


15' 
30' 
30' 
45' 


Distances 

MO  425.0  feet 
NO  430.5  feet 
PO  395.3  feet 
RO  512.6  feet 


UNIVEKSLCY  OF   CALIFQhillA  EXTENSION   DIVISION 
CORRESPONDENCE  CCUHSES  IN  ENGINEERING  SUBJECTS 

Course   1A  Elements  of  Surveying  Stafford 

Assignment   14 

ADJUSTMENT  OF  IIvSTRUMLMTo      (Cont.) 

(114)    (D)   AEJuSTiaENTS  UF   i'KE  K><YE-LEVEL 

Adjustments  of  the  Viye-level  are  made  the  same  as  those  of 
the  dumpy  level  in  cases  v.-here  they  are  of  the  same  nature.      TITO 
adjustments  of  the  Wye,    however,  are  peculiar  tc  that  instrument, 
and  must   receive  special  treatment. 

( 1)  T_o  make  the  bubble -tube   lie  _in_  the  jame  plane  with  the  axis 
of  the  wyes. 

Raise  the  clips  thrt  hold  the  telescope  tube;  turn  the  tel- 
escope through  a  small  angle  by  rotating  in  the  wyes.      If  the  bubble 
remains  at   its  raid-point,   no  adjustment  is  needed;   if  not,   raise  or 
lower  the  end  of  the  bubole-tube  by  means  of  the   screws  that  control 
its   lateral  motion,   until  the  bubble  returns  to   its  mid-position. 
It  nay  require  two  or  more  trials  to  do  this.      (See  A— 1,  First  Ad- 
justment. ) 

( 2)  _T£  make  t^he  axis  c>f_  the  wyes  perpendicular  t_o  the  vertical  axis. 
Level  up  the   instrument  and  turn  180°  upoa  the  vertical   axis; 

bring  the  bubble  one  half  way  oacK  ta  center  Dy  means  of  leveling- 
screws  and  adjust  to  center  by  raising  or  lowering  one  of  the  wyes 
by  means  of  the  capstan  screws  supporting  the  wye.  Repeat  the  ad- 
justment to  insure  accuracy.  (See  A-5,  Third  Adjustment.) 

L5)    (E)   ADJUSTMENTS  OF  THE  TRANSIT 

A  coaplete  transit,  that   is,    ons  having  a  bubble-tube  on  the 


ADJUSTMENTS   OF  THE   WYE  LEVEL 

PZELIMINAPY  ADJUSTMENTS  :- 

Same  as  for   the  clumpy  /eve/. 


Fii?5T  ADJUSTMENT  :-  Line  of  sight. 

To  make  line  of  sight  coincide  with  the  axis  of  the  collar^ 
Without  leveling  set  cross- hairs  on  a  distant, 
point  "o" .   devolve  telescope  ha/f-way  around  in 

the  wyes,  (not  end  for  end)  intersection  now  appear 

,  •   » 
at  v  . 

TO  COFPECT  EPPOP      By  means  of  the  capstar 
screws   that  move  the  cross -hair  ring  bring   th< 
intersect  ion   of  the  cross -hairs   to  a  point  mid- 
FK5.VI  way  between  V 'and  "o". 

When  this  adjustment  is  accomplished  the  intersection  c 
the  cross- hairs  will  remain  fixed  on  one  point  throughout  o 
complete,  rotation  of  the  telescope, 


. 
ADJUSTMENT .-  Bubble 

(a)    To  make  the  axis  of  the  bubble-tube  parallel    to  // 
bottom  of  the    wyes, 

,5ottom  of  wyes __n— -^   Horizontal  Jine 

Axjs_  of  bubb|e:tube 
Horizontal   line  .         .  .      . 

Level  up  ana  clamp 
horizontal  mot/on. 


FIG.VE 


'     - 


Fio.vnr 


Unfasten  clips,  remov^ 
telescope  from  the  wyes,  tun 
end  for  end,  and  replace  in  v* 


a  *           if 

1  T 

~1_        t 



Axis 

J 

of  bubble  -tube 

FIG.K 


bubble  half- way 
back  to  center  by  mean?   of 
adjusting  screws    at  end  of  bu- 
tube. 


Bottom   of  wyes 
Axis  of  bubble-tube 

Center  bubble  by  me> 
of  leveling  screws. 


FIG.X 


(b)    Id  make   the  axis  of  the  bubb/e-tube  lie  in  the  same 

plane  with  the  axis  of  the  collars- 
Level  up  and  clamp  horizontal  motion.  Loosen  clips,  ther, 

swing  bubble- tube   through  small  angle  by  revolving  telesco/st 

If  the  bubble  moves  away  from  the  center  it  should  be  adjustea 
TO  COFFECT  EWOP    Bring  the  bubble  all  the  way  back 

the  center  by  means    of  the    capstan    screws    which    control 

the  lateral  motion   of  the  bubble- tube, 

(cj     Repeat  bubble  adjustment   (a) , 

Note:-  If  the  collars  are  the  same  size  these  aajustm] 
will  make  the  axis  of  the  bubble -tube  parallel  to  the  line  of  s, ' 
This  is  an  indirect  method  of  making  the  adjustment,  for  a  di.i 
method  u$e  the  "peg  adjustment  ", 


THIPD  ADJUSTMENT :-    Wyes. 

To  make  the  axis  of  the  bubble -tube  perpendicular 
the  axis   of  rotation ,   or  vert/'ca/  axis    of  instrument, 


FIG.  XI 


FIG.  xii 


FIG.XHI 


J [ 


Horizonfeil   line 


FIG, 


Bottom  of  wyes 


_____  - 

Axis  of  bubble  -tube 

l"i$~"  Center   bubble  by  men, 

of  leveling  screws, 


Horizontal   line' 

'A     ' 
L.  ~  ~  ~~^~         l~  -  - 

f(/ 


instrument  end 


ax/5  of  rotation, 
error  (24>)  15   twice   the   true 

w. 


Horizontal   line 

'  --W-  Bring  buhble  half-way* 

'~  i  r    ., 

to  center  by  mean^  of  the  law 
capstan  nuts  at  the  end?  of  /e 
I  eve/  bar, 


Bottom  of  wyes 


Level   bar 


Center  bubble   by  mi 


of  leveling 


Eiem.    of  Surv.    1A  Acsignment  14  Page  2 

telescope   and  a  vertical  arc  in  addition  tc  the  usual   plain  instru- 
ment  (Plate   III,  Assignment   IX)    is  preferred  for  the  work  described 
hers,   but  the  surveyor  should   learn  to  adjust    "any  old"  instrument 
that  he  may  be  called  upon  to  use,    for  all  adjustments  become  more 
or  less  deranged  by  the  action  of  the  elements,    etc.,   or  by  rough 
or  careless  usage,    or  through  accident. 

Preliminary : 

Set  up  the  transit   in  an  open  space,  about   200  to  400  feet 
long,   on  as  nearly   level  ground  as  possible,   preferably  in  the 
shade.      Place  the   instrument  over  a  huo  or  stake  set  in  the  ground 
by  means   of  the  plumb-bob;   center   it  over  a    definite  point  in  the 
hub.      This  done,    it   is  unnecessary  to   select  any  other   initial 
point  throughout  many  of  the  adjustments  that  follow;   if  the  in- 
strument  is  removed  to  any  other  setting  during  a  given  adjustment, 
this  new  setting  should  then  be   sufficiently    identified  for   occu- 
pancy at  any  later  time. 

( 1 )  Jto  make  the   plate  bubble-tubes  parpendicul&r  t o  the  vertical 
axis  of  i^he   instrument  : 

Put  one   of  the   level-tubes  parallel  to  a  pair  of  diagonally 
opposite  foot-screws;  this   orings  the  other  tube  parallel  to  the 
remaining  pair  of  screws.     By  manipulating  the  foot-screws  as  di- 
rected for  the   leveling  instrument,   Assignment  XIII,   Art.    113, 
bring  each  bubble   to  the  middle   of  its  tubs;   turn  the  plate  on  the 
lower  spindle  through  1330,  which  rill   reverse   ooth  ouOoles  over 
their  respective    set  of  foot-screws,  an.?,  note  the   position  of  each 


f 
Elem.    of  Surv.    1A  Assignment   14  Page  3 

bubble  in  turn.      If  they  are  at  mid-point  for  each  position,   no 
adjustment  is  necessary;    if  not,   bring  either   (or  both)    bubbles 
one-half  way  back  to  center   by  means  of  the  foot-screws    aid  then 
exactly  to  center  by  means  of  the   screws  that  hold  the   level-tutoe 
to  the  plate.     Repeat  the  whole  process  for  test  and  subsequent 
adjustment  -   one  repetition   is  not  always  enough. 

Some   of  the  adjustments  to  follow  do  not   require  thie 
bubblertube-on-plate  adjustment,    but  any  other  adjustment   is  made 
with  greater  facility  and  assurance  when  this   is  done.      This  se- 
cures a  normal  position  of  the  transit   (i.e.  vertical  axis  truly 
vertical),  which  is  always  desirable.      In  some  transits  one  of 
the  bubble-tubes  just  spoken  of  as   situated  on  the  horizontal 
plate,    is  not  so   situated,    but   is  attached?  to  a   standard  that 
supports  the  horizontal  axis   (the  trunnions)   of  the  telescope; 
the  principle   is  the   same,   however,   and  the  elevated  position  of 
this   level-tube   in  no  v»ay  affects  the  result. 

(2)   To  make  the  upright  cross-hai  r  vertical : 

Direct  the   line  of  sight  to  some   sharply  defined  point  at 
about  50  ft.   from  the  instrument;  focus  one  end  of  the  upright 
hair  exactly  upon  it;   and  then,   Dy   turning  the  telescope   tube  on 
the  trunnions,   note  whether  the  point    "tracks"  upon  the  cross-hair. 
If  it  does,  no  adjustment   is  needed;    if  net,    loosen  all  four  screws 

by 

that  hold  the  cross-hair  reticule,  and  turn  it  around  gently  tapping 
the  screws.     Reset  the   screws,   but   t?e  very  careful  not   to  over- 
strain arty   of  them  in  eo  doing.      In  the  acsence   of  a  convenient 


Elem.    of  Surv.    1A  Assignment   14  Page  4 

point  for  sighting  upon,  a  plumb-line  may   be  suspended  and  used 
instead.     Although  this  plumb-line  requires  more  time  and  trouble, 
it  is  sometimes  preferred.      If  the  horizontal  cross-hair  is  placed 
(as   it  should  be  by  the  maker)  at  right  angles  to  the  upright  one, 
the  horizontal  hair  is  now  in  adjustment  also.      However,    it  is  more 
important  .that   the  vertical  cross-hair  be  truly  vertical;  hence 
the  reason  for  testing  and  correcting  this  one  primarily. 


^o  make  the  line  £f  sight   lie  _in  a  plane  _at   right  angles  to 

the  horizontal  axis  of  the  telescope  : 

requires 
This       />       two  adjustments  -   (a)  When  the   line  of  collimation 

X 

of  the  telescope   is  horizontal;   (b)  when  the  line  of  collimation 
is  in  any  other  position  in  altitude. 

(a)  With  transit  set  over  a  fixed  hub  P  as  described  in 
(1)   direct  the   line  of  sight  toward   a  point  A  about  200  ft.    distant 
and  at  a^out  the  same  elevation  as  that   of  the  telescope  (H.I.    of 
transit).      Turn  the  alidade  plate   180°  about  the  vertical  axis  and 
set   another  point  B  at  about  the  same   distance  as  for  A  and  at  H.  !• 
Now  invert  the  telescope   (plunge  it)  and  sight   again  upon  A.      If  A 
is  bisected  by  the   line   of  sight,    the  adjustment   (a)   is  correct; 
if  not,  olamp  the  instrument  and    set  a  marker  A'    in  the  line  of 
sight  near  A.      Take   1/2  of  the  distance  AA1,  and  set   if  off  from 
A  toward  A';  call  this  point  D.     With  the  plates  and  the  telescope 
both  clamped  in  position,    loosen  the  right  and  left  screws  that 
hold  the  cross-hair  reticule,    aid  tighten  the   one  that  will  bring 
the  vertical  cross-hair  over  the  point  D. 


Eleou  of  Surv.  1A         Assignment  14  Page  5 

Note:  To  test  this  adjustment,  three  points  in  line  through  P,  at 
H.I.  ,  "will  be  on  a  straight  line.  Every  position  of  the  telescope 
when  bisecting  one  point  will,  by  reversing  or  plunging  (inverting) 
also  bisect  the  other  point. 

(b)  Set  up  the  transit  in  a  locality  where  observation  may 
be  made  on  some  high  point.  A,  as  the  top  of  a  tall  building,  a  spire, 

or  a  flag-pole,  and  carefully  level  the  plate.  As  this  adjustment 

for 
is  to  correct  the  intersection  of  two  vertical  planes  the  point 

aloft  should  be  high,  but  not  at  a  great  horizontal  distance  from 
the  instrument.   Sight  first  upon  the  high  point;  clamp  the  plates 
while  bisecting  the  point,  turn  the  telescope  on  ite  horizontal 
axis  (in  the  trunnions),  and  sight  a  marker  placed  at  a  convenient 
distance,  if  possible  directly  below  A  and  at  about  the  elevation 
of  the  center  of  the  instrument  (H.I.  ).  Call  this  point  on  the 
ground  B.  Reverse  on  either  spindle,  plunge  the  telescope  and 
again  bisect  A»  the  point  aloft.   Turn  the  telescope  down  on  the 
trunnions  and  direct  toward  B;  if  B  is  bisected  by  the  line  of 
sight  the  horizontal  axis  is  in  adjustment;  if  B  is  not  in  the 
line  of  sight  place  another  marker  B  »  in  line  near  B.   The  ad- 
justment is  then  made  by  raising  or  lowering  the  movable  end  or 
trunnion  of  the  horizontal  axis,  by  means  of  the  adjusting  screws 
in  cap  at  movable  end,  until  the  line  of  sight  bisects  the  point 
midway  betweefa  B  and  B*.  Go  through  this  whole  process  a  second 
time  for  test  and  subsequent  adjustment. 


Elem.  of  Surv.  1A          Assignment  14  Page  6 

(4)  12  adJust  the  Level  _on  Telescope. 

This  may  be  done  by  the  Peg  Method  describee  in  connection 
with  the  Dumpy  Level,  used  likewise  with  the  Wye  level.   (See 
Assignment  XIII.)  A  simple  method  of  making  this  adjustment  is  the 
following:   Set  two  stakes  A  and  B_  at  the  same  level.   This  can 
be  done  by  choosing  a  nearly  level  stretch  and  carefully  setting 
the  stakes  by  means  of  the  transit  telescope,  or  better,  by  means 
of  an  engineer 'e  level.   Or  if  a  sheet  of  water  of  considerable 
extent  may  be  near  e.t  hand  this  may  be  used  for  determining  a 
level  line  by  driving  the  stakes  so  that  each  projects  one  or 
several  inches  above  the  surface  and  at  the  same  level.  Now  with 
the  transit  set  up  and  most  carefully  leveled  near  A,  sight  on  a 
target  set  at  H.I.  on  Bj  adjust  the  level  on  telescope  by  means  of 
the  screws  that  hold  it  to  the  telescope,  bringing  the  bubble  to 
the  center.  For  test  and  subsequent  adjustment  set  up  at  B  and 
observe  on  target  set  at  H.I.  on  A.   (Here  H.I.  means  height  of 
the  line  of  collimation  at  intersection  of  vertical  axis,  i.e., 
the  center  of  the  instrument.) 

(5)  T£  adjust  the  Vernier  Index  of  the  Vertical  .arc. 

With  the  telescope  bubble  exactly  in  adjustment  and  at  the 
center  of  its  run,  and  with  plate  levels  in  perfect  adjustment, 
loosen  the  screws  that  hold  the  vernier  of  the  vertical  arc  (or 
circle)  and  move  until  the  0  or  index  (A)  coincides  exactly  with 
the  proper  limb  division,  0  or  180°.   If  there  are  t\vo  opposite 
verniers,  both  should  be  adjusted  to  read  exactly  0  and  180°  when 
both  the  telescope  and  its  level  are  horizontal  and  in  adjustment. 


• 


Slem.  of  Surv.  1A          At  signment  1.4  Page  7 

This  adjustment  is  important  and  most  convenient,  out  by 
no  means  essential,  as  the  vernier  error  nay  be  observed  without 
moving  it  into  correct  adjustment  and  applying  this  as  correction 
to  readings  of  vertical  angle  for  every  case,  adding  or  subtracting 
the  correction  ae  circumstances  may  require.   Some  transits  have  a 
small  level  attached  to  the  vernier  of  the  vertical  arc,  which  ob- 
viates the  adjustment  betv/eea  telescope  level  and  arc,  as  this 
level  and  arc  adjustment  is  difficult  to  make  and  therefore  trouD- 
lesome. 

(6)  Adjustment  or  the  Gradienter. 

This  is  made  when  the  preceding  adjustments  are  made. 
Loosen  the  swinging  arm  (a  sort  of  lever)  that  is  actuated  by  the 
gradienter  screw,  which  is  likewise  the  tangent  screw  to  the  hori- 
zontal axis.   Move  the  milled  head  and  knife  gauge  both  to  zero 
and  then  tighten  the  arm  upon  the  trunnion.  Be  sure  that  the 
settings  of  any  of  the  transit  parts  concerned  in  this  adjustment 
are  not  disturbed  in  making  this  adjustment. 
116)  GENERAL  OBSERVATION  ON  ADJUSTING 

Besides  remembering  that  the  adjustment  of  instruments  is 

/ 
of  great  importance,  you  should  give  attention  to  other  things 

necessary  in  sound  practice. 

First.   The  adjustments  just  descrioed  for  the  transit  snould 
be  gone  over  in  the  order  they  are  grven,  unless  it  is  obvious  thp.t 

•  some  of  them  are  correct  and  hence  do  not  require  attention. 
Some  adjustments  can  not  be  made  until  certain  ones  precedent 


Eleu.  01'  Surv.  IA          Aesigmnent  14  Page  8 

thereto  have  been  made;  e.g.,  adjustment  3b  must  follow  3a  to  accom- 
plish the  correction,  and  therefore  3a  should  at  least  be  tested  out. 

Second,.   The  order  of  procedure  in  any  particular  adjustment 
•will  be  (1)  the  desired  relation:  (?)  the  test;  (3)  the  method  of 
adjusting;  (4)  a  final  test,  usually  made  with  greater  care,  which 
will  prove  of  immense  satisfaction  to  the  careful  engineer. 

Third.   In  making  nmy  alteration  by  loosening,  tightening, 
or  shifting  screws  or  other  parts,  do  all  in  a  workmanlike  manner. 
A  slotted  screw  should  be  turned  with  a  screw-driver  that  fits 
the  slot,  a  capstan  screw  with  a  pin  that  fits  the  hole  in  it, 
milled-head  screws  with  the  thumb  and  finger,  not  with  pliers  or 
a  wrench.   Never  leave  screws  loosened  where  they  should  be  firm, 
nor  overstrain    them  in  tightening  them. 

Fourth.  Tfnen  a  general  overhauling  of  an  instrument  is 
required,  do  not  attempt  to  bring  any  given  part  into  perfect  ad- 
justment oy  a  "once-  over",  but  proceed  by  making  the  series  of 
corrections  as  accurately  as  possible  in  the  order  given  above. 
Mien  the  whole  series  has  been  followed  out,  return  to  number  one 
an3  repeat  each  one  for  test.   Of  course  if  test  does  not  reveal  that 
the  error  has  been  corrected,  repeat  the  process  necessary  to  accom- 
plish this. 

(117)  (F)  ADJUSi&Ei^S  OF  THE  SOUR  AXiACEivENT  (Saegmuller).   (See  Plate 
VIII,  Assignment  XII.) 

These  adjustments  must  be  made  after  attaching  the  solar 
upon  the  transit  telescope. 


Elein.    of  Surv.    1A  Assignment   14  Page  9 

Preliminary . 

See  that  the   screw  that  connects  the   solar   is  turned  down 
to  a  firm  position.      Bring  the    levels  of  the  alidade  plate  to  cen- 
ter and  also  the   level   on  transit  telescope;   set   the   index  of  the 
vertical  circle. 

(1)  To  raake  the  axis   of  the  bubule-tuibe  in    the  solar  telescope 
parallel   t_o  t.he  axis  _or  the   same.      Thie    is  accomplished  exactly 
as  for  the  transit  telescope  by  the  method  of  reversion. 

( 2)  To  make   the   polar   ay. is  _o£  the   solar   in   line  with  the   vertical 
axis  of  the   transit. 

lie   sure  that  the  transit's   vertical  axis   is  truly  vertical, 
then  bring  the  bubble   of  the   solar  telescope  to  center,    and  test 
for  all   positions  through  360°.      If  not   in  adjustment,   employ  the 
method   of  reversion. 

(3)  To  make  the    lines  £f  collimation  _in  the  two  telescopes   parallel. 
With  the   preceding  adjustments   fully  made,    sight    ooth  tele- 
scopes upon  a  vertical    line    (   a   suspended  plumb   line   or  corner   of 

a  building)  at    100  feet  or  more  away.      Clamp  the  telescopes  in  this 
position  and  carefully   level  the   bubble   on  transit  telescope  so   as 
to  bring  the   lines   of  sight   of   Doth  telescopes  into  the  same  plane. 
Now  measure   the   distance   between  the  exes   of  the  telescopes  along 
the  polar  axis.      Draw  two  distinct  parallel   lines  on  a  piece  of 
paper,    or   better,    of  cardboard,    at  this   same  distance  apart.      Fasten 
up  the  card  with  the   lines  horizontal   at   100  feet  or  more  away,   and 
at  the  same   level,    end  direct  the  telescopes  toward  it,   aligning 


Elein.    of  Surv.    1A  Assignment   14  Page   10 

the  transit  cross-huir  upon  -che  lower  line.  The  solar  cross-hair 
should  then  be  on  the  upper  line  when  its  bubble  is  at  center;  if 
not,  alter  the  position  of  the  cross-hair  reticule  in  the  solar 
telescope  until  this  is  accomplished.  Test  by  revolving  the  whole 
instrument  around  upon  the  spindle  cf  the  lor.-er  plate  of  transit. 
The  bubbles  of  the  alidade-plate,  the  bubble  of  the  transit  tele- 
scope, End  also  that  of  the  solar  telescope  should  remain  at  cen- 
ter for  all  positions  rhrough  360°.  The  lines  of  sight  of  both 
telescopes  should  intercept  the  same  interval  (that  between  their 
axes)  at  all  distances.  All  seven  adjustments,  two  of  the  solar 
and  five  of  the  transit,  must  be  made  with  scrupulous  care  to  se- 
cure satisfactory  results  when  using  the  solar. 

))    (G)   ADJUSTMENTS  OF   THE  FLAKE-TABLE 

Plane-tables  embody  the  same  parts  as  the  transit.  The  lev- 
eling head  corresponds  to  the  similar  part  in  the  transit;  the 
board  or  planchette  to  that  of  the  lower  plate;  the  ruler,  sur- 
mounted with  sights  or  telescope,  to  the  alidade  of  the  transit. 
The  levels  are  variously  attached;  some  have  only  one  level  upon 
the  ruler,  others  hrve  two  levels  at  right  angles  so  attached, 
while  still  others  have  no  level  attached  to  the  ruler,  bat  are 
furnished  with  a  bar-level  that  cay  be  placed  at  any  desired  po- 
sition on  the  board,  for  the  purpose  of  adjusting  the  table  to  a 
horizontal  position. 

(1)    i'he  adjustment   of  the  leveling  device      in  any  case   is  ac- 
complished  by  the  method   of  reversion,    the      levels     after      oeing 


Elem.  of  Burv.  1A         Assignment  14  Page  11 

turned  through  180°  are  brought  half  way  to  center,  first  by  the 
leveling  head,  then  by  the  level  adjusting  screws.   In  case  of  the 
bar- level  the  adjustment  may  be  made  in  a  manner  similar  to  that 
described  for  the  carpenter's  level  in  Assignment  XIII. 

( 2 )  £o  make  _the_  vertical  c  ircle  (arc)  read  zero  when  the  tele- 
scope bubole  is  at  center. 

Carefully  level  the  telescope  and  set  the  vernier  index  at 
zero  of  the  arc. 

(3)  To  make  the  edge  of  the  ruler  a  true  fiducial  line. 
Upon  a  smooth  surface  draw  a  fine  pencil  line  the  full 

length  of  the  ruler;  reverse  the  ruler  end  for  end  setting  it 
against  the  line  and  note  whether  the  line  and  the  ruler  edge 
again  coincide,   -tf  not,  the  edge  should  be  straightened.   This 
requires  skill  and  necessary  tools;  the  instrument  maker  is  the 
best  one  to  do  this.   If,  as  might  happen,  one  half  of  the  ruler's 
edge  curves  in  one  direction  aid  the  other  half  in  the  opposite 
direction  (i.e.  half  is  concave,  half  convex),  a  reliable  test  is 
to  move  each  half  along  the  line  to  the  opposite  part;  the  devia- 
tion in  either  portion  will  then  immediately  reveal  itself. 
(119)       In  conclusion  on  the  subject  of  adjustments  a  few  generali- 
zations are  here  presented. 

Be  sure  that  any  adjustment  is  required  oefore  making  it, 
and  that  the  method  is  fully  understood  before  attempting  any  al- 
terations, and  then  use  the  proper  means  and  proper  tools.  A 


Elera.  of  Surv.  1A          Assignment  14  Page  12 

novice  should  always  work  under  the  advice  and  direction  of  someone 
having  the  Knowledge  and  skill  necessary  in  any  case. 

Needless  taking  of  instruments  apart,  cutting,  filing  or 
scraping  parts  to  fit  or  attempt  to  repair  and  adjust  them  must 
never  be  done  except  in  extreme  cases.   Generally  send  the  instru- 
ment to  the  maker. 

Good  work  can  often  be  done  with  instruments  out  of  adjust- 
ment, provided  the  user  knows  how  to  determine  certain  relations. 
For  example,  the  plate  levels  ueed  not  be  in  adjustment  provided 
one  knows  what  position  their  bubbles  should  have  when  the  vertical 
axis  is  truly  vertical.   For  the  horizontal  plate  is  horizontal  if 
the  plate  bubbled  remain  in  the  same  positions  in  their  tubes 
throughout  a  complete  revolution.  Again,  the  line  of  sight  need 
not  be  parallel  to  the  axis  of  the  level  on  telescope  provided  the 
index  of  the  vernier  of  the  vertical  arc  (circle)  is  at  zero  when 
the  line  of  sight  is  horizontal;  the  converse  condition  is  also 
permissible  provided  one  knows  and  applies  the  index  error  of  the 
vertical  circle. 

Again,  in  running  levels  with  an  engineer's  level  or  transit, 
it  is  enough  that  the  level  (attached  to  the  telescope-  in  either 
instrument)  be  at  the  middle  of  its  run,  or  any  other  del inite  po- 
sition, when  taking  sights  at  equal  distances^  from  the  instrument. 

But  the  liability  to  error  is  too  great,  and  corrections  are 
too  easily  neglected  in  all  such  cases,  and  it  is,  therefore,  always 


Elem.  of  Surv.  1A 


Assignment  14 


Page  13 


best  to  have  instruments  fully  and  nicely  adjusted.   It  is  in  such 
conditions  that  work  can  be  done  easily,  rspidly,  and  with  the 
satisfactory  assurance  that  the  liability  to  instrumental  error 
has  been  mostly  eliminated. 

Among  the  problems  set  for  student  work  several  will  be 
given  in  the  v,-ork  of  adjusting. 


REFERENCES : 


Tracy  pp.  581-606 

Raymond  pp.  63,  79,  108 

Johnson  pp.  15,  63,  86,  102 

Breed,  H.  ,  pp.  25,  56,  70,  89,  Vol.  I 


QUESTIONS: 

1.  The  needle  of  a  compact  is  bent*   Hov«  may  the  error  in 
bearing  from  this  cause  be  eliminated? 

2.  In  compass  use  v;hich  of  the  two  plate  levels  is  more 
important  and  why?  (Give  reasons) 

3.  How  may  a  temporary  setting  of  the  plates  of  a  transit 
in  a  horizontal  position  be  secured  without  adjusting  the  plate 
levels? 


4.  If  a  transit  has  a  full  vertical  circle,  ho^'  may  a  level 
line  be  determined  without  the  aic  of  the  level  on  telescope? 

5.  How  may  a  level  line  be  determined  by  use  of  a  transit 
in  the  absence  of  a  vertical  circle  and  a  level  on  telescope? 


UNIVERSITY  OF  CALIFORNIA  EXIENSION  DIVISION 
CORRESPONDENCE  COURSES  IN  ENGINEERING  SUBJECTS 

Course  1A  Elements  of  Surveying  Stafford 

Assignment  15 

kEIHODb  OF  LAND  SURVEYING 
FOREWORD 

This  assignment  will  set  forth  the  several  methods  of  Land 
Surveying,  explain  the  purposes  of  such  surveys,  and  give  details 
of  the  procedure  in  each  case. 
(120)  PURPOSES  OF  UND  SURVEYING 

(a)  To  lay  out  the  bounding  lines  and  locate  their  intersection; 
to  fix  necessary  points  so  that  they  may  be  identified  and  re-lo- 
cated by  reference  to  certain  known  or  established  lines  or  points; 
to  sake  a  record  in  the  form  of  notes  of  data  used  in  the  survey; 
and  to  map  such  a  survey  in  suitable  manner. 

(b)  To  retrace  the  lines  and  the  angles  of  any  survey,  and  to 
re-establish  any  or  all  points  in  this  survey  for  the  purpose  of 
identifying  the  various  features  of  a  tract  or  parcel  of  land. 

(c)  To  measure  established  lines  and  angles  of  any  tract  for 
the  purpose  of  determining  the  content  or  area  of  such  tract. 

(d)  To  run  lines  in  extent  and  direction  for  the  purposes  of 
eub-dividing  or  "parting  off"  of  lands  by  parcels  either  in  form 
or  content. 

Land  surveys  nay  be  executed  either  by  use  of  the  compass 
and  chain,  as  in  ferin  trectr;  or  by  transit  and  taps  in  cases  re- 
quiring more  refined  iueat>urements,  as  in  city  surveying.   (See 
Assignment  XXVI  on  City  Surveying. ) 


Elem.  of  Surv.  1A          Assignment  15  Pag®  2 

(121)       Since  in  most  cases  the  tract  of  land  to  be  laid  out  or 

surveyed  forms  part  of  the  U._  S.  Public  Land  Survey ,  it  is  necessary 
to  follow  established  lines  of  such  survey.   This  requires  a  know- 
ledge of  the  methods  and  practice  of  the  Public  Land  Surveys,  which 
will  be  treated  in  Assignments  XIX  and  XX  of  this  course,   The  work 
of  the  surveyor  in  such  cases  is  to  reproduce  the  lines  and  points 
as  established  by  the  Public  Land  Survey.  This  becomes  a  simple 
matter  of  identifying  certain  points  previously  set. 

As  an  example  of  this,  suppose  that  a  certain  tract  is 
described  as  the  N.  E.  Quarter  of  Section  23,  Township  2  North, 
Range  3  East,  Mt.  Diablo  Meridian  and  Base.   Here  is  clearly  a 
case  of  identifying  township  and  section  corners.   The  number  of 
the  Township  (2  North)  and  Range  (3  East)  are  the  first  important 
designations  and  these  constitute  the  co-ordinates  necessary  for 
locating  the  region  of  this  particular  tract  of  land  which  is 
further  described  as  being  the  Northeast  portion  (1/4  ecfuare 
mile)  of  Section  Number  23- 

The  nearest  Township  corner  is  the  Southeast  corner  of 
T2  N,  R3  E  of  Mt.  Diaolo  Base  Line  monument  and  is  north  6  miles 
and  east  18  miles  from  said  B.L.  monument.   Thence  to  the  south- 
east corner  of  Section  23  is  two  miles  north  by  one  mile  west 

where  the  southeast  corner  of  Section  23  should  be  found.   Then, 

C!.LXC 
by  measuring  80  chainsAaorth,  the  northeast  corner  of  section  23 

is  also  identified.   Jf  the  point  40  chains  north  from  the  south- 
east corner  was  located  in  the  running,  of  the  line  northward,  it 


Elem.  of  Surv. 


Assignment  15 


Page  3 


may  now  be  checked  by  measuring  southward  from  the  northeast  cor- 
ner and  n  proper  monument  established.  Also  the  northwest  corner 
must  be  determined  by  measuring  westward  from  the  northeast  corner 
of  Section  23  a  distance  of  40  chains  and  checking  by  measuring 
the  full  80  chains  (1  mile)  to  the  northwest  corner  of  Section  23- 
A  monument  is  set  at  the  40  chain  point.   Thence  measure  40  chains 
south  and  check  by  measuring  40  chains  east  to  the  first  1/4  section 
division  established  on  the  east  line  of  Section  23.  All  this  is 
necessary  since  the  Public  Land  Survey  sets  monuments  only  at  sec- 
tion corners  and  at  quarter-section  points  on  boundaries  of  sections. 

interior 

All/\quarter  section  corners  must  be   located  on  the   land  by  the    local 

surveyor. 

A  reference  to  the  shaded  quarter  section  in  Section  23  of 
the  adjoining  diagram  of  a  township  will  further  elucidate  the 

foregoing  description  and 

/  Sac.  13 

-ic 


Sec.  15 


See.  22 


Sec.  27 


Sec.   14   / 
ch 


1/4  Sec/" 


hC 
v 


Sec.  24 


Sec.  25 


o. 


•S.ec.  26 


procedure. 

The  function  of  the 
U.  S.  surveyor  was  completed 


Figure  37 


with  the  establishment  oy 

^ 

o 

^r         him  of  the  sect; on  corner 

Sec.  25    monument e;  the  local  sur- 
veyor usj.ng  tbvc-s  monuments 
sets  the  quartei -section 


corners  for  his  client.   A  knowledge  of  the  methods  er.d  practice 
of  Surveys  of  the  Public  Land  is  estential  to  the  surveyor  who 


Elem.  of  Surv.  1A         Assignment  15  Faga  4 

would  do  work  worthy  of  an  expert  and  faithfully  serve  those  em- 
ploying him.  As  a  large  variety  of  problems  of  the  nature  of  the 
foregoing  present  themselves  for  solution,  you  are  advised  to  ac- 
quaint yourself  with  the  instructions  furnished  by  the  General 
Land  Office  of  the  U.  S.  as  no  specific  instructions  are  furnished 
from  any  other  source. 

Deeds  to  lands  give  descriptions  from  which  the  surveyor  ia 
required  to  retrace  or  lay  out  the  property  lines  showing  the  po- 
sition of  corners  and  giving  the  angles  or  bearings  of  lines. 
These  descriptions  usually  name  the  parcel  or  lot  of  land  and 
often  give  "metes  and  bounds"  which  are  the  lengths  ard  directions 
of  lines  bounding  the  tract.  From  the  data  so  supplied  the  sur- 
veyor goes  into  the  field,  sets  up  the  instrument  at  a  corner  of 
the  property  that  is  distinctly  marked  (or  perhaps  most  convenient ) 
and  proceeds  to  measure  angles  and  courses  as  set  forth  in  the  de- 
scription.  It  is  his  function  to  reproduce  to  the  best  of  his 
ability  the  points  and  lines  there  given  and  to  mark  by  proper 
stakes  of  other  means  these  points  upon  the  land.   At  least  one 
prominent  corner  should  be  tied  in.   That  is,  two  or  more  points, 
the  bearing  and  distance  of  which  are  carefully  measured,  are 
chosen  and  described  in  order  that  the  point  so  tied  may  be  readily 
relocated,  should  the  stake  or  monument  marking  it  be  removed. 

A  farm  or  city  lot  which  is  to  be  fenced  or  on  which  build- 
ings or  other  improvements  are  to  De  erected  should  be  carefully 
surveyed  before  beginning  such  improvements.   The  location  of  the 


Elem.  of  Surv.  1A          Assignment  15 

corners,  fence  lines  <*nd  sitee  of  buildings,  ditches,  drainage 
lines,  etc.,  can  consistently  form  £  part  of  such  survey,  and 
should  be  executed  with  a  precision  in  accordance  with  the  im- 
portance of  the  work.   Carelessness  in  this  regard  has  often  been 
the  cause  of  serious  and  expensive  mistakes  and  has  led  to  trouble 
and  litigation,  which  a  correct  survey  would  have  prevented.   This 
is  especially  true  of  divisional  lines  in  both  farm  and  city  prop- 
erty, especially  in  the  latter  where  buildings  are  frequently  made 
to  follow  property  lines. 

In  case  a  survey  is  to  be  made  to  relocate  the  points  and 
lines  of  an  old  survey  where  the  bearings  are  given  with  relation 

to  the  magnetic  meridian,  it  is  essential  that  the  former  declina- 
nation  of  the  magnetic  needle  be  shown.    Should  the  declina- 
tion at  time  of  the  original  survey  be  a  part  of  the  record  (which 

should  be  noted  on  the  original  notes,  but  unfortunately  is  not 
always  so)  and  should  the  present  declination  also  be  determined, 
this  becomes  a  simple  matter.  But  in  the  absence  of  such  data  they 
must  faithfully  be  recomputed  for  proper  guidance  in  the  survey. 
Assignment  VI  on  Compass  Surveying  gives  adequate  instruction  for 
this  purpose,  but  at  least  one  course  should  be  rerun  on  the  ground 
for  the  purpose  of  fixing  such  course  with  respect  to  the  resurvey 
and  of  properly  orienting  the  property.   Any  variation  of  the  dec- 
lination should  be  correctly  applied  to  every  course  in  the  re- 
surveys. 

The  surveyor  has  no  warrant  for  establishing  points  or  run- 
ning lines  otherwise  than  as  given  in  the  original.  This  my  not 


m.  of  Surv.  1A          Assignment,  15  Page  6 

apply  in  case  of  a  monument  or  stake  that  may  Oe  lost  or  obliterated, 
in  "which  case  the  surveyor  relocates  and  reports  the  restoration 
of  such  monument  to  the  oest  of  his  ability  and  in  conformity  with 
the  remaining  features  of  the  survey  in  which  the  locations  are 
known  and  distinct.   (See  Assignment  XL  on  the  Judicial  Functions 
of  the  Surveyor . ) 

Each  survey  for  location  or  resurvey  should  embody  in  the 
report  a  full  and  complete  set  of  notes  and  in  most  cases  a  map  of 
the  tract,  showing  tie  lines,  witness  marks,  courses  in  bearing 
and  distance,  interior  angles,  and  any  explanatory  remarks  that 
may  render  the  notes  clear  and  intelligible  to  others.  A  clearly 
executed  sketch  is  usually  made  a  part  of  the  notes  and  should 
not  be  omitted  when  needed  to  ciarify  otherwise  obscure  or  ambigu- 
ous data.  A  little  care  in  this  matter  often  adds  to  the  value 
of  the  report  and  obviates  the  necessity  of  much  labor  otherwise. 

The  survey  of  a  tract  for  the  purpose  of  finding  the  content 
or  area  constitutes  a  third  purpose  and  consists  generally  in  re- 
running the  courses,  measuring  the  distances  and  checking  the 

is 
points  upon  the  tract  of  land.   If  the  survey  for  area  only,  it 

is  not  essential  that  attention  be  given  to  the  orientation  or 
even  to  the  declination  provided  the  corners  of  the  tract  can 
otherwise  be  readily  located.   In  such  case  the  oearings  and  dis- 
tances as  related  to  the  form  of  the  tract  itself  are  sufficient. 
However,  it  is  most  expedient  that  the  survey  for  area  be  conducted 


Elem.  of  3urv.  1A          Assignment  15  Page  7 

in  the  usual  manner  by  traversing  with  compass  and  chain,  or, 
v;here  special  accuracy  is  required,  with  transit  and  tape. 

Bearings  may  be  either  magnetic  or  true  bearings.  Where 
the  latter  are  to  be  taken  with  the  compass,  it  is  convenient  to 
set  off  the  declination  with  the  variation  arc  and  to  take  such 
bearings  directly  in  the  field.   These  may  be  computed,  however, 
from  recorded  magnetic  bearings  in  lieu  of  setting  off  the  variation. 

The  surveyor  should,  if  practicable,  traverse  the  entire 
traet,  set  up  at  each  corner,  take  the  back  and  forward  bearings, 
and  check  by  measuring  interior  angles.   He  should  measure  all 
sides  of  the  field.   If  it  contains  any  meander  lines  such  as  those 
of  large  streams,  ponds,  or  lakes,  a  set  of  eff-sets  from  a  meas- 
ured straight  line  to  the  meander  should  be  measured  and  charted. 
In  measuring  across  streams  and  bodies  of  water  or  across  ravines 
or  past  any  unavoidable  obstruction  sufficient  data  should  be 
taken  in  the  field  to  enable  a  correct  computation  to  be  made 
subsequently.  Hence,  check  up  all  such  data  taken  in  the  field 
before  leaving  it  and  be  assured  that  such  are  Tall  and  correct. 
This  will  simplify  the  office  work. 

Upon  completion  of  the  survey  the  error  of  closure  should 
be  noted.   This  may  be  determined  by  measuring  the  distance  from 
the  end  of  the  last  course  as  taken  in  the  field  to  the  point  of 
beginning  of  the  first  course  end  dividing  this  small  distance  by 
the  measured  perimeter  of  the  fie.'d.   If  this  error  of  closure 
exceeds  1  in  500,  the  measurements,  especially  of  doubtful  courses, 


. 
•     • 

. 


Elem.  or  ourv.  1A          Assignment  15  Page  8 

should  be  repeated  for  check  or  correction.   In  case  of  transit 
surveys,  where  great  accuracy  is  required,  this  error  of  c losure 
ought  not  to  exceed  1  in  5000  or  perhaps  1  in  10,000.   The  error 
of  closure  depends  upon  both  the  angle  measurement  and  the  line 
measurement,  and  when  ooth  are  made  -.vith  equal  care,  the  error 
should  be  distributed  accordingly.  Check  lines,  such  as  diagonals, 
are  often  of  value  in  locating  the  presence  of  ervor  and  where 
time  or  expense  are  not  too  great  these  lines  should  be  measured. 
Too  great  pains  cannot  be  taken  where  precision  is  required^ 

(122)       Two  other  methods  of  survey  for  area  (a)  measurement  of 

sides  with  a  sufficient  number  of  diagonals  to  divide  the  figure 
into  geometric  figures  convenient  for  computing  their  areas.  Most 
all  fields  may  be  divided  into  triangles  by  a  suitable  number  of 
diagonals  joining  non-consecutive  vertices.   In  such  case  the 
trigonometric  formula  -  Area  (of  each  triangle)  -  i/S(S-a)(S-b)(S-c) 
where  a,  b,  c,  are  the  lengths  of  the  sides  and  S  =  1/2  (a-fb+c). 
Frequently  the  computation  is  simplified  when  a  rectangular  or 
trapezoidal  portion  may  be  measured  off. 

If  any  portion  be  bounded  oy  irregular  curved  lines  as  in 
case  of  the  meander  of  a  stream  or  body  of  water,  etc.,  suitable 
off-eets  should  be  made  fron.  a  straight  diagonal  line  and  the  area 
computed  and  added  to  the  remainder  of  the  field.  Assignment  XVII 
will  consider  in  raore  detail  the  mathematical  methods  of  computing 
areas. 


Elera.   of  Surv.    1A  Assignment  15  Page  9 

(123)  The  remaining  method  of  surveying  for  area   (b),   by  a  single 

set-up  of  the  instrument,  may  now  t>e  considered. 

Select  any  convenient  point  within  the  field  or  at   one 
corner,   if  suitable   triangles  can  be   laid  out  from  such  setting: 
measure  the  angles   (bearings)   formed  by  lines  radiating  from  the 
point  occupied  to  the  corner  of  the  field;   also  measure  the   lines 
including  these  angles  and  by  trigonometry  compute  the  areae  of 
all  the  triangles  formed  ty   the  sides  of  the  traverse  and  the 
radiating   lines.     The  total  angle    about  a  central  set-up  »ill  of 
course  be  360°  and  is  a   convenient  check  for  the  angle  measurement, 
but   is  by  no  means  absolute ^   the  discrepancy  should  be  small.      If 
the  set-up  is  made  at   one  corner  then  the  interior  angle  at  this 
corner  should   ae  measured  as  a  check. 

The  trigonometric  formula  for  computing  area  in  this  case 

ie     Area  =  1/2  the  product  of  the   including  sides  and  the   sine  of 

0/3 
the   included  angle.     Example:     Given  in  the  triangle^the   sides  OA, 

"I3,    and  the  angle  0;  then  area  - 

1/2  OA  x  03"  x  sin  0. 


B 


Fig.    38 
When  employing  the  method  of  a  single   set-up  it   is  most 

convenient  to  take  stadia  measurements  oi  the  radiating  lines, 
which  are  usually  sufficiently  accurate  for  the  uses  of  such  surveys. 

These   last  two  methods    (a)   with  tape   only,    and   (b;   by  a   single 
set-up  are  quite  suitable  for  obtaining  the  areas  covered  by  crops, 
meadow  lands,   etc.,   and  are  especially  applicaole  to  measurements 


Elem.    01    Surv.    1A  Assignment   15  Page   10 

of  such   lands  when  devastated  by  fire,    or  for  estimating  the  ex- 
tent of  damage  for  insurance  companies,   railroads,   and  others 
interested  in  loss   adjustment. 

(124)  The  subject  of  subdivision  and   parting-off  of  land  will  be 

specially  treated  in  a  suosequent   assignment   (XVIII)    but  a  few- 
general  directions  are  given  here. 

Before  proceeding  to  a  subdivision  it  is   essential  that  a 
full   end  correct  survey  and  nap  of  the  entire  tract  be  made,    if 
such  is  not  already   available.      This   survey  should  show  the   loca- 
tion of  all  corners  with  a  suitable  number  of  tie-lines,   courses 
of  boundaries,  meanders,    roads,   buildings,  and  other   improvements. 

In  the   office  the   suDdi visions  should  be  determined  by 
measurement  or  computation  and  if  expedient  should  be  clearly 
charted  upon  the  map.      ?he  actual  subdivisional  survey  should  be 
the   locating  of  these  protracted  points  and  lines  upon  the  land, 
marking  the  same  with  convenient  monuments  or  stakes  of  a  more  or 
less  permanent  character.      If  portions  are  to  be  set   aside  for 
public  or  joint  communal  use,    such  as  roads,   lanes,  streets,   or 
parks,  the  proper  designations  must  be  shown  upon  the  map  and 
staked  out  in  the   field. 

It. is  sometimes  required  to  subdivide   into  aliqout  parts  - 
halves,   thirds,   fifths,    etc.    in  the  distribution  of  estates  as 
devised  by  will  or   otherwise,    or  to  part-off  such  proportional 
parts  as  may  be  required.      Here   the  problem  becomes   one   of  a  math- 
ematical nature.      As  these  prooiems  are  purely  geometric   or  sat 


Elem  of  Surv.  1A          Assignment  15  .   Page  11 

most  trigonometric  in  their  scope,  it  is  unnecessary  to  deal  with 
them  here. 

When  the  divisional  lins  is  to  be  run  perpendicular  to  a 
given  side,  as  a  line  of  road  or  street,  or  parallel  to  a  given 
side,  or  otherwise  in  direction,  the  "falling"  of  the  line  and  its 
direction  must  be  first  determined  and  such  lines  AE  are  required 
to  accomplish  this  ere  then  accurately  staked  off  in  the  field. 
(See  Assignment  XVIII  on  "parting  off"  of  land.) 

References : 

Breed  &  Hosmer,  Vol.  I,  Chap  V. 
Tracy,  Chap.  XII. 
Raymond,  Chap.  VII, 
Johnson,  Chap.  VII. 

QUESTIONS: 

1.  Explain  how  a  line  maybe  prolonged  where  an  obstruction, 
such  as  a  building,  stands  upon  a  line. 

2.  How  may  a  line  j)ro longed  across  a  river  or  other  body 
of  water? 

3.  Shov;  how  a  parcel  of  land  may  be  surveyed  by  traversing 
when  the  corners  cannot  "be  occucied  owing  to  fences  or  buildings. 

4.  Explain  the  use  of   random  lines  in  surveying.  What 
do  you  understand  by  the  slope  or  off-set  of  such  a  line? 


OF  CALIFORNIA  EXIENSIOK  DIVISION 
CORRESPONDENCE  COURSES  IN  ENGINEERING  SUBJECTS 


Course   1A  Elements   of  Surveying 

Assignment   16 

LATITUDES  AMD  DEPARTURES  CO-ORDINATES 

FOREWORD  : 

The  positions  of  points  in  a  plane  are  often  conveniently 
expressed  by  the  distances  from  certain  assumed  axes,  which  are 
the  co-ordinates  -  to  the  right  or  left,  abcissae;  above  or  below, 
ordinates.   Since  the  bearings  of  lines  are  chosen  with  respect  to 
a  meridian  (either  true  or  magnetic)  the  common  designation  of 
rectangular  co-ordinates  is  conveniently  made  the  distance  north 
or  south  on  the  meridian,  called  latitude  and  the  distance  east 
or  west  from  the  meridian,  called  departure,   ihe  present  assign- 
ment will  explain  the  manner  of  so  representing  courses  in  sur- 
veying and  the  application  of  co-ordinates  to  Land  Surveying. 


125) 


the 

R 

A 


The  course  AB  in  Figure  39  is  defined  oy  giving  the 
angle  of  bearing  9  and  the  distance  AB_.   The  latitude  {distance 

north  on  the  meridian)  Am,  is  found  by 

~  ~~rr *—*  '  f  '         f.  rt 

Bultiplying  A3    (course  distance)   by  the 

cosine   of  0.      The  departure   (distance 
east   froa   the  meridian)   An,    is   found  by 
multiplying  AB    (course   distance)    by  the 

.    sine   of  0. 

>E 

Here   the   Gearing  of  course  AcJ   is 

northeast,   or  we   ssy   it   lies   in  the   N.E. 


D*  pa  st  use „. 


Fig.  39 


i.  of  3urv.  1A          Assignment  16  page  2 

quadrant;  in  this  case  the  latitude  is  a  north  latitude  and  the 


departure  is  an  east  departure.   Had  the  bearing  been  ^Q°Vi,  then 
the  latitude  would  also  be  a  north  latitude,  but  the  departure 
would  be  a  wesfe  departure. 

So  also  in  the  S.E.  quadrant  the  latitude  is  south,  the 
departure  east;  in  the  S.W.  quadrant  the  latitude  is  south,  the 
departure  west. 

For  convenience  latitudes  north  are  plus,  latitudes  south, 
minue  ;  departures  east  are  plus,  departures  west,  minus.  When 
entering  into  computations  these  signs  are  always  prefixed. 

North  latitude  and  south  latitude  are  also  called  northings 
and  southings  respectively;  east  and  west  departures  are  known  as 
eastings  and  ge  at  ings,  respectively. 

The  latitude  then  is  the  product  of  the  distance  into  the 
cosine  of  the  bearing;  and  if  north,  it  is  positive  (t-),  if  south, 
it  is  negative  (-). 

Lat.  =  Dist.  x  cos  Bearing. 

The  departure  is  likewise  the  produce,  of  the  distance  into 
the  sine  of  the  bearing;  and,  if  east,  it  is  positive  (f)  ;  if  west, 
it  is  negative  (•<•). 

Dep.  =  Dist.  x  sin  Bearing. 

In  Figure  40,  the  angles  by  bearings  and  the  latitudes  and 
departures  are  graphically  represented. 

The  course  AB  has  N.  Lat.  -  S,  B.  Dep.  -  6;  these  may  also 
be  taken  as  the  lines  Em  snd  Am  respectively. 


Blem.    of  ourv.    1A 


Assignment    16 


page   3 


D 


10 


Distances   and 
Bearings   of  Courses 

Course  Bearing  Distance 

A  -  B  N  e°  E  92  +  62 

B   -  C  S  0     E  132  +    42 

10      C   -  D  S  P    W  102  +  102 

D   -  A  N    7"W  92  +  5£ 

Calculation  of  Distances 


Figure   40 


A  -  B   =     vTl?     - 
B    -  C   = 
C   -  D  = 
D   -  A  = 
Calculation  of  Angles  of  Bearing 

©  =  33°41.'5  Tan  6  =  6/9  =  0.6667N 
0  =  18  00.3  "  $  -  13/4  =3. 2500  / 
P-  45  00.0  *  /»  =  10/10  =  L  0000  ("  Natural  Functions 

T=  38  00.6      "  T   =  9/5  =   1.8000J 

Tabulation  of  Results 


10.82 
13.60 

14.14 
10.30 


Course 

Bearing 

i  _ 

A 

-  B 

33°41.' 

5 

10. 

82  ch.      9.00                       6. 

00 

+9.0 

+6.0 

B 

-  C 

72 

53. 

8 

13. 

60    "                         3.99      13. 

00 

-4.0 

+13. 

0 

C 

-  D 

45 

00. 

0 

14. 

14    "                      10.00 

10. 

00 

-10.0 

-10. 

0 

D 

-  A 

60 

56. 

7 

10. 

30    "         5-00 

9. 

00 

+5.0 

-9.0 

A  -  B 


C-D 


D  -  A 


Lat. 

9. 

002 

3. 

989 

9. 

999 

5. 

002 

Lat. 

log 

Lat. 

0. 

95<137 

0. 

60079 

0. 

99994 

0. 

69916 

log 

Lat. 

log 

cos 

9. 

92014 

9. 

46725 

9. 

84949 

9. 

68632 

log 

cos 

log 

Dist. 

1. 

03423 

1. 

13354 

1. 

15045 

1. 

01284 

log 

Dist 

log 

sin 

9. 

74407 

9. 

98035 

9. 

84949 

9. 

94159 

log 

sin 

log 

Dep. 

0. 

77830 

1. 

11389 

0. 

99994 

0. 

£5433 

log 

Dep. 

Dep. 

6. 

002 

12 

.999 

9. 

999 

9. 

002 

A  -  B 


B   -  C 


C-D         D  -  A 


;I'j:n.  of  burv.  1A 


Assignment  16 


Page  4 


The  computation  of  latitudes  and  departures  from  the 
course  (given  angle  of  bearing  and  distance)  is  much  shortened 
by  logarithmic  method.   The  formulae 

Lat.  -  Dist.  x  cos  Bearing,  and 
Dep.  •=  Dist.  x  sin  Bearing, 

are  conveniently  put  in  the  logarithmic  form  as  f ollows  : 
log  Lat.  =  log  Dist.  +  log  cos  Bearing,  and 
log  Dep.  =  log  Dist.  +  log  sin  Bearing. 

Example : 

Given  bearing  N23°45'E,   distance  463.7  ft.     To  compute 

the  latitude  and  Departure.      Arrange  in  the  following  convenient 

form: 

Lat.  =  424.43  (a)  Add  (c)    and  (d)  which  give   log  Lat., 

log  Lat.  =       2.62761  (b) 

log  cos  Bear.  =       9.96157  (c)  then  the  anti-log  is  424.43,   (a), 

log  Dist.  -       2.66624  (d) 

log  sin  Bear.  =       9.60503  (e)  Again  add  (d^)  and  (e);  this  gives   log  Dep., 

log  Dep.  -       2.27127  (f) 

Dep.  =  186.75  (g)   (f),   and  the  anti-log  is  186.75,    (g). 

Cases   involving  the   latitudes  and  departures  of  a  number 
of  courses  may  be  worked  out  by  arrangement  in  successive  columns, 
the   letters  designating  each  course  written  at  the  top  (and  bottom) 
of  its  respective  column.      The   arrangement  is   shown  in  the  example 
of  a  closed  traverse  displaced  in  Figure  40. 

The  sum  of  the   latitudes  of  any  closed  traverse   is   zero. 
Likewise  the  sum  of  the  departures  of  any  closed  traverse  is   zero. 
Or  expressed  in  mathematical  language 

r  Lat.   =0;     2.  Dep.   =  0. 


Elem.  of  Surv.  1A          Assignment  Ifc  Page  5 

In  traversing  the  field  the  surveyor  will  go  as  far  north 
as  he  does  south,  and  as  far  east  as  ha  does  west.   This  may  also 
be  put  in  the  familiar  terms : 

The  total  northing  is  equal  to  the  total  southing;  and  the 
total  easting  is  equal  to  the  total  westing. 

If  the  latitude  (or  departure)  of  any  course  is  wanting,  it 
may  be  found  Dy  subtracting  the  sum  of  the  given  north  latitudes 
(or  east  departures)  from  the  sum  of  south  latitudes  (or  west  de- 
partures), the  algebraic  difference  being  the  missing  co-ordinate. 

(126)  ERRORS 

Should  the  latitudes  or  departures  not  balance,  i.e.,  should 
the  sura  of  the  north  latitudes  Qe  greater  or  less  than  the  sum  of 
the  south  latitudes,  the  amount  of  such  difference  is  called  the 
error  in  latitude;  likewise  any  discrepancy  in  the  departures  is 
the  error  in  departure. 

The  errors  in  latitude  and  departure  having  been  determined, 
it  is  then  necessary  to  find  the  lineal  amount  of  error  of  closure. 
This  last  is  the  hypotenuse  of  the  right  triangle  of  which  the 
sides  about  the  right  angle  are  the  error  in  latitude  and  the 
error  in  departure.   Hence  the  lineel  error  in  closure  is  the 
square  root  of  the  sum  of  the  squares  of  theee  two  co-ordinate 


quantities.   Ihue  lineal  error  of  closure  =  y(error  in  lat)^  + (error  in 

+  d2 


Bleu,  of  Surv.  1A          Assignment  16  -Page  8 

The  error  of  closure  is  usually  expressed  as  a  ratio  -  the 
lineal  error  divided  by  the  perirr.eter  of  the  traverse. 

Error  of  closure  =     1 

perimeter 

Suppose,    for   example,   that  the  sum  of  the  north  latitudes 
and  sum  of  the  south  latitudes  differ  by  15  links,    and  the  sums  of 
the   east  and  lyest  departures  differ  by  20  links,   the  total   perimeter 
ol  the  traverse  being  99.12  chains;  then 


•=      y/152  +  20k  =  25;   and 


Error  of  closure  =  . £?  ,  which  is  usually  expressed  in  a 

9912 

fraction  with  numerator  unity.   This  is  found  by  dividing  Doth 
numerator  and  denominator  by  the  number  expressing  the  numerator 
of  the  above  fraction,  E]..   In  this  case  25  *  25  =  1.   9912  *  25  ~ 
396+,  or  nearly  400.   Hence  we  say,  the  error  of  closure  is  one 
in  400;  i.e. ,  EC  =  1/400. 

This  error,  1/400,  is  a  very  large  error.   In  compass  surveys, 
the  error  of  closure  should  never  exceed  1/500,  and  is  seldom 
greater  than  1/2000.   A  transit  survey  error  of  closure  should 
evidently  be  much  less  than  this;  1/lQpOO  is  a  maximum,  end  often, 
as  in  city  surveys,  1/40,000  is  sought. 

The  error  of  closure  may  be  due  to  errors  in  angle  measure- 
ment, which  usually  occur  when  the  angles  measured  lie  between 
lines  that  are  short,  or  when  measuring  angles  r»ith  the  compass. 
(See  Assignment  VI,  Compass  Surveying.)  The  error  may  result 
from  difficulty  in  measuring  lines,  a  failure  to  keep  the  tape 


Elem.  Of  Surv.  1A          Assignment  16  Page  7 

taut,  or  failure  to  level  it  over  uneven  ground.   Also,  mistakes 
may  occur  in  reading  the  tape,  although  these  may  usually  be  de- 
tected from  gross  discrepancies  that  should  be  removed  by  remeas- 
uring  the  courses  in  which  such  mistakes  seem  to  occur. 

(127)  ADJUSTING  LATITUDES  AND  DEPARTURES 

Before  proceeding  to  use  latitudes  and  departures  in  com- 
putations, or  for  mapping,  they  should  be  adjusted  proportionally, 
so  that  the  northings  and  southings,  and  eastings  and  westings 
balance.   This  is  generally  called  "balancing  the  survey",  and 
the  adjusted  co-ordinates  are  called  "balanced  latitudes",  "bal- 
anced departures". 

Balancing  is  accomplished  by  distributing  the  error  in 
latitude  and  also  the  error  in  departure  proportionally  to  their 
respective  co-ordinates.   The  errors  in  line  measurement  usually 
result  in  measuring  the  line  top  long,  as  may  be  seen  when  we 
consider  that  errors  here  arise  from  sag,  alignment,  and  lack  of 
tension.   Therefore  it  is  better  practice  to  deduct  from  the 
greater  side  than  to  add  to  the  lesser. 

Errors  in  Angle  Measurement.  Where  measurements  of  angles 
are  made  with  compass  the  error  may  be  large,  5'  to  15',  through- 
out the  course.  Such  error  should  be  distributed  in  parts  to  the 
respective  angles  in  which  error  is  most  likely  to  occur.  Angles 
measured  by  the  transit  are  more  precisely  determined,  and  differ 
oy  a  few  seconds  or  one  or  two  minutes;  these  errors  when  small 
may  be  applied  to  the  most  doubtful  angle.  In  any  case  where  the 


Elea.    oi'Surv.    1A  Assignment   16  Page  8 

error   in  angle   showF    a  gross  mistake   (a  blunder   in  reading),   as  for 
example  where  angle  measure  does  not  check  with  magnetic   bearings, 
a  remeasurement  of   angle  should   be  made. 

In  all  these  considerations  it  is  necessary  that  every  angle 
and  every  line   should  be  measured  in  the  field,    as  any  part  omitted 
while  it  may  _be_  supplied  by  computation  explained  further  on 
(Assignment  XVIII),   no  check  can  be  hacl  upon  the  work  and  hence 
the   attempt  to  adjust    latitudes    and  departures   is  futile. 

In  balancing  the    latitudes  and  departures  of  a  compass 
survey  the  following   rule   is  applied: 

Having  determined  the  latitude  error,    subtract  such  propor- 
tional part  of  the  error  from  each  computed   latitude  as   the   length 
of  its  course  bears  to  the  perimeter  of  the  field.     Also  to  adjust 
departures  subtract  a  proportional  part  of  the  error   in  departure 
from  the  departure   of  each  course,      the   corrections  in  all  cases 
should  be  applied  in  such  a  way  as  to  reduce  the  difference  between 
the   sums   of  the  two  columns,    so  that  the    resulting  difference   is 
zero;   i.e.,   the  sums  balance. 

In  a  transit   survey  the   correction  is  made  by  proportional 
parts   of  the  error    in  the   latitude   or  departure  to  each  course,   as 
compared  with  the  total  latitude  or  total   departure  without   regard 
to  algebraic   signs. 

This  subject  may  best  be  explained  by  taking  a  concrete 
example  and  following  the  computations,  step  by  step.  As  such 
example,  we  take  the  data  of  the  following  traverse,  a  chain  and 


Eieau    01    3urv.    1A 


Assignment   16 


Page  9 


compass  survey  of  a  quadrangular  field.   The  data  given  are  the 
course,  bearing  and  distance. 


A  -  B 

B  -  C 

C  -  D 

D  -  A 


Balanced 

Bearing 
N45°30'E  : 

Dist. 

K  .  Lat  . 

S.Lat. 

E.Dep. 

W.Dep. 

Lat. 

Dep. 

2.87 

2.01 

2.05 

+2.01 

+2.05 

S51°10'E 

5.05 

3.17 

3.93 

-3.19 

+2.93 

S53°10'W 

4.63 

2.44 

3.93 

-2.45 

-3.94 

N29°15'W 
Totals 

4.16 

3.63 

2.03 

+3.63 

-2.04 

16.71 

5.64 

5.61 

5.61 

5.98 
5.96 

5.96 

0.00 

0.00 

Error 

in  Lat 

.   0.03 

0.02  s 

Error 

in  Dep. 

Error   of  closure  =  V.032  +  .022  =  0.036;   i.e.  ,    1/464 

The   logarithmic   computations  are  given  for  the    latitudes  and 
departures  recorded   in  the  above  table   in  the  following  scheme: 
Course  A-B  B-C  C-D  D-A 


Lat. 

2.01 

3.17 

2.44 

3.63 

log  Lat. 

0.  30354 

0.  50060 

0.  38776 

0.  55985 

log  cos 

9.84566 

9.79731 

9.72218 

9.94076 

log  Dist. 

0.45788 

0.70329 

0.66558 

0.61909 

log  sin 

9.85324 

9.89152 

9.92921 

9.68897 

log  Dep. 

0.31112 

0.59481 

0.59479 

0.  30806 

Dep. 

2.05 

3.93 

3.93 

2.03 

Course 

A-B 

3  -  C 

C-D 

D-A 

N 


Figure   41 


Elem.    of  Surv.    1A  Assignment  16  Page   10 


Problea: 

As  an  exercise  in  computing  and  tabulating  the  data,  in  the 
computation  of  latitudes  and  departures,  and  in  balancing  them  use 
the  data  given  in  Figure  41. 

REFERENCES : 

Tracy  Pages  384  -  398 
Raymond  "  141  -  148 

Johnson  "  185  -  193 

Breed  &  Hosmer     "  400  -  408,  Vol.  I 


UNIVSRSIiY  OF  C/.LIFORKIA  EXTENSION  IdVISIOI; 
CORRESPONDENCE  COURSES  IN  ENGINEERING  SUBJECTS 

Course  1A  Elements  of  Surveying  Swafford 

Assignment  17 

Double  Meridian  Distances  -  Areas 
FOREWORD 

This  assignment  will  explain  the  meaning  and  computation  of 
Double  Meridian  Distance,  Double  Parallel  Distances,  and  the  Com- 
putation of  Areas. 

(129)  DEFINITIONS 

The  Meridian  distance  of  a  line  is  the  horizontal  distance 
of  its  middle  point  from  the  meridian  (line)  of  reference.  This 
meridian  of  reference  may  be  the  magnetic  meridian,  the  true  me- 
ridian, or  any  assumed  line. 

In  Figure  42,  the  line  MN  has  a  meridian  distance  equal  to 
Ch  which  joins  the  mid-point  of  MN  and  is  perpendicular  to  the  me- 


ridian of  reference  XY.  Ma  is  the  north  latitude,  aN  the  east 
.X 
a 


Figure     42. 


departure.     But  Ch  =  1/2  aN; 
i.e.,    the  departure  of  the 
course  MN   is  double  the  merid- 
ian distance  (D-M.D. )   ae  de- 
fined above.     Hence  to  find  the 
double  meridian  distance  of  the 
first  course   take   the   departure 
of  that  course.      D.M.D.    of  MN  = 
aN.      The  meridian  distance   of 
the  course  BO  is  bj,   the  per- 
pendicular from  the  mid-point 


Elera.    of  Surv.    1A  Assigr.mert  17  Page  2 

of  NO  to  the  meridian  of  reference  XY.     But  bj  =  1/2  (aN  +  dC) , 
since  the   line   joining  the  mid-points  of  the  non-parallel  sides 
of  a  trapezoid  is  parallel  to  the   bases  and  equal   to  one-half  the 
sum  of  the  bases.      That,   is,   aN  +  dls;  -r  sO  =  2  bj   (since  dO  =  ds  +  sO). 
In  other  words,   the  D.M.D.    of  the  second  coarse   is  equal  to  the 
departure   of  the    first   course  plus  the  D.fc.D.    of  the  first  course 
plus  the  departure  of  the   second  course. 

D.M.D.    of  JJO  =  jaH  +  aN  (=  dsj   -r  sO. 

The  meridian  distance  of  _OP  is  ek,   the  perpendicular  from 
the  mid-point   of  OP  to  XY.      ek  =  1/2,  (gP  +  dp),   which  is  to  say, 
that  £k  joining  the  mid-points  of  the  non-parallel  sides  of  the 
trapezoid  dppg  is  equal  to     one-half  of  the  parallel   sides.     Hence, 
the  D.M.D.    of  OP  =  2ek  =  gP  +  dO.     But  gP  -  dt  =  do  -  tO,    aid 
_dp_  =  aN  +  sO.      Therefore,    by  substitution, 

D.  it  D.    of  OP  =  dO  -   tO  -f  aN  +  sO 

=  aN_  +  _eO  -  tO  -f  aN  +   sQ 
=  ^ [  -t-  aN  +  sO  -t-  sO  -  to 

But  aN  •*  aN_  +  £0  =  D.  M.  D.    of  the   second  course,    and  -to  =:  departure 
of  the  third  course,  which  is  a  west  departure,   and  therefore 
negative.      Lastly,    by  construction,    fl   is   the  meridian  distance 
of  the  course  MP  and   is  equal   to   1/2  gP.      Consequently  the  D.  M.  D. 
of  the   last  course  is   ,    like  the  D.  M.  D.    of  the  first  course,    equal 
to  the  departure   of  that  course.      Or  thus  : 

D.  M.  D.    °f  £M  =  2  £1  =  gP  =  dt. 


Elem.  of  Surv.  1A          Assignment  17  Page  3 

Computing  from  the  previous  course, 
D.  M.D.  of  FM  =  D.  M.D.  3rd  C  •*•  Dep.  3rd  C  +  Dep.  4th  C. 

=  2afl  +  2sO  -to  +  (-to)  +  i'g£)»  but  gP  =  dt 
=  2dO  -  2 to  -dt 
=  dt  =  gP 

This  value,  gP,  you  will  note,  is  equal  to  the  departure 
of  the  last  course  but  of  contrary  sign.  This  is  true  of  any 
closed  traverse  and  is  a  convenient  check  upon  the  computations  of 
the  D.  M.D. 's  and  should  always  be  observed  to  that  end.   Of  course 
it  is  required  that  the  latitudes  and  departures  are  adjusted;  i.e., 
balanced. 

We  will  now  take  up  the  specific  case  of  a  simple  traverse, 
showing  the  computation  of  the  double  meridian  distances. 

Course  Bearing  Dist.  N.Lat.  £.  Lat.  E.Dep.  W.pep.  D.M.E. 

A  -  B   S35°32'E  8.6  ch.  7.0  5.0  5.0 

B  -  C  N71°34'E  9-5   "  3-0  9-0  19.0 

C  -  D  N18°26'B  12.7  "  12.0  4.0  32.0 

D-E  Due  West  11.0  "  0.0  11.0  25.0 

E  -  A  S41011'W  10.6  "  3.0  7.0  7.0 

-,15.0    15.0     18.0   18.0 

•=^  I— X 

balanced 

It  will  be  noted  that  the  latitudes  aid  departures  balance, 
and  we  shall  now  proceed  with  the  computations  as  follows: 


Elem,  of  Surv.  l.i.         ^Rsisuiusnt  1  Page  4 


5.0  D.  M.D.  of  1st  course  (=  Dep.  of  that  course) 

5.0  Dep.  of  1st  course 
9.0    "   of  2nd   " 

19.0  D.M.D.  of  2nd  course 

9.0  Dep.  of  2nd  course 
4.0    "   of  3rd  course 

32.0  D.  M.  D.  of  3rd  course 

4.0  Dep.  3rd  course 

-11.0  Dep.  4th  course 

25.0  D-M.D.  of  4th  course 

-11.0  Dep.  4th  course 

-  7.0  Dep.  5th  course 

7.0  D.  M.D.  5th  course.  This  is  numerically  equal  to  the 

departure  of  the  5th  (last)  course,  but  of  contrary  sign.   There- 
fore, the  computation  checks. 

(130)  RULE  FOR  COMPUTING  D.M.D.  's 

(a)  The  D.M.D.  of  the  first  course  is  the  departure  of  that  course. 

(b)  The  D.M.D.  of  the  second  course  is  the  sum  of  the  departure 

of  the  first  course,  the  D.M.D.  of  the  first  course, 
and  the  departure  of  the  second  course. 

(c)  The  D.  M.  D.  of  the  nth  course  is  the  sum  of  the  D.  M.  D- 

of  the  (n-l)th  course,  the  departure  of  the  (n-l)th 
course,  and  the  departure  of  the  nth  coarse. 

(d)  The  D.M.D.  of  the  last  course  is  numerically  equal  to 

the  departure  of  the  last  course,  but  of  contrary  sign. 

(131)  AREAS 

By  referring  to  the  traverse  MMOPM,  Figure  42  of  this  aseign- 
raent,  it  will  be  seen  that  the  figure  there  shown  is  composed  of  the 


3 1  tin.  GJ.''  3urv.  i.',  ',sff5.0;  „ ,:  t  r.7  Page   5 

trapezoids  aNQd  and  dQPg ,  which  together  include  the  area  of  the 
field  plus  the  areas  of  the  triangles  aNM  and 


The  area  of  the  trapezoid  is  equal  to  the  product  of  the 
meridian  distance  into  the  latitude,  or  twice  the  area  of  each 
trapezoid  is  the  product  of  the  D.M.D.  of  any  course  into  the 
latitude  of  that  course.   It  will  be  seen  that  certain  of  these 
products  are  positive  and  others  negative. 

By  choosing  the  meridian  of  reference,  XY,  through  the 
extreme  west  point,  M,  the  resulting  signs  of  all  the  D.M.D. 's 
are  positive,   ficnce,  the  products  of  D.M.D-  's  and  s outh  latitudes 
will  be  minus  areas,  and  the  products  of  D.M.D. 's  and  north  lati- 
tudes will  be  plus  areas.   The  difference  between  the  minus  areas 

therefore 
and  plus  areas  willAbe  the  area  of  the  field.   This  then  gives  us 

the  Rule  for  Computing  the  Area  o£  the  Field  from  Latitudes  end 
D.M.D. 's  as  follows: 

(a)  Multiply  the  latitude  of  each  course  by  its  D.M.D. 
hadng  regard  to  sign. 

(b)  The  algebraic  sum  of  the  products  is  the  double  area; 
divide  by  2  to  find  the  area. 

If  the  course  distances  have  been  measured  in  chains,  the 
products  will  be  square  chains.   This  may  be  reduced  to  acres  by 
dividing  by  10,  since  10  sq.  ch.  =  1A.   Simply  remove  the  decimal 
point  one  place  toward  the  left. 

Had  the  lines  of  the  traverse  been  measured  in  feet,  the 
resulting  area  would  have  been  square  feet;  and  since  43,560  sq.  ft. 


Elein.    of  Surv.    1A 


Ajssignraent   1? 


Page  6 


equal  1  A,  to  reduce  to  acres,  divide  by  this  number  (43..560;. 

The  following  is  a  tabulation  of  the  latitudes,  departures, 
D.M.D. 's  and  products  of  the  five  course  traverse  contained  on  a 
previous  page : 


Course 

A  -  B 

B  -  C 

C  -  D 

D  -  E 

E  -  A 


Bearings 

and 

Distances 
omitted 


Lat. 


Pep. 


-  7.0  •*•  5-0 
+     3.0  +  9-0 
+  12.0  +  4.0 

0.0  -  11.0 

-  8.0  -  7.0 


B.  to.  D. 

+  Prod. 

-  Prod. 

5.0 

35.00 

19.0 

57.00 

32.0 

384.00 

25.0 

0.00 

7.0 
Totals 

56.00 

441.00 
91.00 

91.00 

2)350.00 

175.00  sq.    ch. 
17.5     acres 


We  now  give  the   following  data,    showing  a  complete  ^tabulation 
of  bearings,    distances ,   etc.    of  the  traverse, of  a  quadrangular  field: 


—  i  —    —  i  — 

! 

A-B 

N84°00  'W 

9.04 

0.945 

8.990  k  0.95  ',-  8.98 

-  8.98 

!  8.631; 

3  -C 

S21°15'W 

12.34 

11.501 

4.472  1-11.50  j-  4.45 

-22.41 

257.  7150  ! 

c  -r 

N72°15'E 

12-92 

3.939 

12.302 

h-  3.95  i+12.32 

-14.54 

67.433* 

D-  A 

H  9°30'E 

6.68 

6.588 

1.105 

;+  6.60  !+  1.11 

-  1.11 

i 
1 

40.98 

11.  472  :  11.  501  !  13.  407  13.462    bTiancedT 

1 
257.  7150  i?3.<i9o'. 

11.  £7?        1R.407                     73.2900 

0.029  0.055 

Error   in  Lat.   Error  in  Dep. 


2)184.4250 


Error  in  Closure  = 


•*  (.06)   =  .067,  or  1/600,  about. 


Blem.    of  Surv.    1A. 


Assignment   17 


Page  7 


Interior  Angles 

A  =  86° 30' 
B  =  105°15' 
C  =  51°00' 
D  =  117°15' 

360°00 ' 


Figure  43. 


Logarithmic  Computation  of  Latitudes  and  Departures 


Courses 

A  -  B 

B  -  C 

C  -  D 

D  -  A 

Lat. 

0.945 

11.501 

3.959 

6.588 

log  Lat. 

1.97540 

1.06074 

0.  59537 

0.81878 

"  cos 

9.01923 

9.96942 

S.  48411 

9.99400 

"  Bist. 

0.95617 

1.09132 

1.11126 

0.32478 

sin 

9.9S761 

9.55923 

9.97882 

9.21761 

"  Dep. 

0.95378 

0.65055 

1.09008 

0.04239 

Dep. 

8.990 

4.472+ 

12.302 

1.105 

Courses 

A  -  B 

B  -  C 

C  -  D 

D  -  A 

Computation  of  D.M.D. 

's 

-  8.98 
-  8.98 
-  4.45 

D.M.D. 

Dep. 
Bep. 

D.M.D. 

Dep. 
Dep. 

D.M.D. 
Dep. 
Dep. 

1st 

It 

2nd 

2nd 
n 

3rd 

4th 

c. 

n 
n 
n 

it 
» 

n 

N 

il 

-22.41 
-  4.45 
+12.32 

-14.54 
+12.32 
+   1.11 

-  1.11  D.M.D.  4th  c. 

The  D.  M.  D-  of  this 
last  course  is  numerically- 
equal  to  the  Dep.  of  the  last  course,  but  of  contrary  sign.  CHECK 

Here  we  have  placed  the  meridian  of  reference  through  A,  at  the 
extreme  east  point  and  using  the  ususl  convention,  east  positive, 


Elem.  of  Surv.  1A          Assignment  17  Page  8 

west  negative,  the  resulting  D.M.D. 's  are  all  negative.   Had  the 
meridian  been  passed  through  C,  the  D.M.D.  's  would  then  be  posi- 
tive; cr,  if  through  B  or  D,  some  would  then  be  positive,  some 
negative.   The  usual  effect  of  such  assumptions  as  the  last  two, 
is  to  complicate  computations  and  this  should  oe  avoided. 

PR031EM  1 

As  an  exercise  for  the  student,  the  following  data  are  given: 
Station     Azimuth     Distance 


A 

107  °15' 

16.4  oh. 

B 

196  c  15' 

24.1    " 

C 

246  °05' 

19.6     " 

D 

13°55' 

37.0    " 

Reduce  azimuths  to  bearings,  compute  latitudes  and  departures, 
and  balance  them;  also  compute  D.M.D. 's  end  areas  in  acres. 

Show  errors  in  latitude  and  departure  and  lineal  error  of 
closure;  also  the  error  ratio. 

Sketch  the  field  approximately  to  scale  and  find  the  interior 
angles.   Use  every  means  of  checking  your  results. 

In  conclusion  you  are  referred  to  other  methods  of  computing 
areas  already  given  in  Assignment  XV. 


• 


Elem.    of  Surv.    1A  Assignment    17  Page  9 

(132)   DOUBLE    PARALLEL  LISTa.MCES 

Instead   of  D-M.D's.   we  .nay  use  double  distances  from  the 
parallel   (or  horizontal  co-ordinate  axis)   and  for   computation  of 
areas  multiply   these   by   the   departures   in   a  manner  similar  to  the 
preceding  method.      In  fact,   where   it  is   desirable  to  check  compu- 
tations,  this  affords   a  valuable  means,  and   it   is    sometimes   so 
employed. 

In  cases  where  B.P.D's.    (double  parallel   distances)   are 
used,    it  is  convenient  to  pass   the  horizontal  co-ordinate   (which 
may  be  called  a.  parallel  of  reference)   through  the  most   southerly 
point   and  thus  all  D.P.D's.  will  be  positive  as  they  will  be 
measured  northward  which,    Dy   convention,    is  regarded  as  plus. 

PROBLEM  2    As  an  illustrative  example  of  this  method  and  for  clearly 
fixing  the  manner  of  computation  of  D.P.D.'e  and  also  comparing 
results  with  these   obtained  from  D-M-B'a.,   the   student   is  here 

given  a  simple  traverse  which   should  be  worked  out    Doth  trays. 

Balanced 
Course       Bearing       Distance       Lat.        Pep.        D.P.D . 

A  -  B  S  60° 15'  E  7.06  ch. 

B  -  C  II  37   15  E  b.93 

C  -  D  N  39   30  W  6-OC 

D  -  E  S  57  45  Yi  4.t5 

E  -  A  S  3u  00  W  4.98 

REFERENCES : 

Tracy  pages  415-416 
Raymond  152-153 

Johnson  185-193 

Breed  &  Hosmer  "        400-404,  Vol.    I 


UNIVEHSIi'Y  OF  CALIFORNIA  EKXENblDK  M.  Vlb  I  ON 
CORRESPONDENCE  OOURSEvS  IN  ENGINEERING  SUBJECTS 

C  CUE  SB  IA  Elements  of  Surveying 

Assignment  18 

V 

SUPPLYING  OMISSIONS   -  PARTING  OFF  LAiMD 

FOREWORD 

Certain  data  wanting  in  any  land  traverse  may  be  supplied 
by  computations  from  the  given  data  under  allowable  conditions, 
and  a  portion  of  thie  assignment  will  treat  of  a  few  cases  of  such 
nature.   The  subject  of  Land  Surveying  as  treated  in  this  course 
will  give  also  a  few  typical  cases  of  dividing  or  parting-off 
land.   Problems  of  both  classes  may  be  given  in  many  forms,  and 
therefore  only  a  limited  number  of  each  will  be  taken  up. 


;i32)  kISbING  DATA 

As  stated  in  the  treatment  of  latitudes  and  departures, 
the  sum  of  the  north  latitudes  ie  (in  any  closed  traverse)  equal 
to  the  sum  of  the  south  latitudes;  also  the  total  east  departure 
is  equal  to  the  total  west  departure. 

Regarding  the  north  latitudes  as  positive  and  the  south 
latitudes  as  negative,  the  east  departures  as  positive  and  the 
west  departures  as  negative,  it  follows  that  the  algebraic  sum 
of  latitudes  is  zero,  and  the  algebraic  sum  of  the  departures  is 
zero. 

Hence  £Lat.  =  0;  £  Dep.  .  =  Q.   Or  to  write  in  extended  form: 

A  cos  c*  +  B  cos£  +  C  cos  c*  •*•  D  cos  c"  =  0   (a) 
A  sin  o<  t  B  sinD  -*•  C  sin  #*+  D  sin  £  =  0   (b) 

where  A,  B,  C,  and  D  are  the  distances  of  the  several  courses  and 
°<  ,  p  ,  o,  and  o  are  the  respective  bearings. 


Elem.    of  Surv.    1A 


Assignment  3.8 


Page  2 


Vie  thus  have  two  simultaneous  equations  and  are  therefore 
aole  to  solve  for  two  unknown  quantities,  whether  they  be: 

1.  Length  and  bearing  of  one  course. 

2.  Length  of  one  and  bearing  of  another  course. 

3.  Lengths  of  any  two  courses. 

4.  Searings  of  any  two  courses. 

(133)       buppose  the  distance,  D,  md  the  bearing  of  the  same  course,  S, 
are  unknown.   (Figure  44) 

Then  D  cos  o  will  equal  the  algebraic  sum  of  the  latitudes 
of  the  remaining  courses  with  their  signs  changed;  in  other  words, 
it  is  the  value  of  the  unknown  term  in  equation  (a)  above. 

In  like  manner  D  sin  S  is  also  found  from  equation  (b). 

o 

The  course  distance  is  now  computed  by  the  formula  Dist  = 

?      ? 
Lat  •*•  Depc;  also  the  bearing  D-A  is  the  angle  whose  tangent  is 

(i.e.  ).   Or  having  computed  the  distance,  D,  the  sine 

Lat  D  cos  $ 

and  cosine   may  Doth  be  found;  the  one  b^   dividing  the  departure 
by  D;  the   other   oy  dividing  the    latitude    by  D.      This  last  method 
furnishes   a  convenient  checJc^upon  computations. 


Fig.    44 


Fig.    45. 


=m.  of  Surv^  1A         Assignment  .16 

(134)  If  ohe  missing  parts  are  two  adjacent  sides,    as  CD  and  DE 
in  Figure  45,   compute  the   length  of  an  auxiliary   line,   CE,    oy  the 
above  method;  then  in  the  triangle  CDE  the    parts  CD  and  DE  may  be 
readily  found,   since  the   side  CE  and  the  angles  E  and  C   are  known. 

(135)  When  the  missing  parts  are   two  non-adjacent  course  distances, 
(Figure  46),   the  following  offers  an  ingenious  solution:     Given 
the  traverse  ABC-- A,    in  which  all    sides  and  bearings  except  the 
non-adjacent   sides  AG  and  BC   are  known;   to  find  AG  and  BC» 

Solution:  Construct  HG 
„  parallel  and  equal  to  AB    and 

^        '      XT, 

draw  HC,  thus  forming  the 
closed  traverse  CDEFGHC.  By 
Case  I  compute  HC. 

In  the  triangle  BHC  we 


now  know  its  angles  and  the 
Fig.  46 

side  HC,  from  which  B_C_  and  BH 

may  be  readily  computed.   3_H  is  equal  to  AG  (the  opposite  sides 
of  a  parallelogram). 

Each  problem  of  this  nature  requires  a  little  study  to 
determine  the  best  method  of  attack,  but  if  the  unknown  parts 
do  not  exceed  two.  the  solution  is  possible.   Indeed  there  are 
certain  special  classes  when  even  three  unknowns  may  be  found 
by  readjustment  of  figure,  but  it  is  not  required  to  enter  upon 
an  explanation  of  such  cases. 


Elem.  of  surv  IA, 


Assignment  18 


Page 


These  methods  ate  useful  in  the  part  ing-  oiT  of  land  treated 
in  the  following  pages  and  a  refereno«  will  be  made  to  this  part 
of  the  assignment  in  the  explanations. 

(136)   PAkXIwG  Or'F  AUL>  SUBLIVILiIM}  LaWD 

Most  of  the  problems  in  the  parting  off  and  subdividing  of 
land  are  purely  geometric.   Many  othere  may  be  solved  by  the  simple 
methods  of  trigonometry,  but  a  few  must  De  dealt  with  by  resort  to 
co-ordinate  meant  similar  to  the  foregoing.* 

Let  it  be  required 
to  cut  off  a  given  area 
from  the  field  ABODE  by 
s.  line  starting  at  the 
corner  E. 

First  cut  off  the 
triangle  EBA  and  compute 
the  distance  E3  and  its 

Figure  *7  bearing.  Deduct  the  area 

of  triangle  EBA  from  the  required  area,  the  residue  will  be  the 
area  of  triangle  EbH,  and  it  is  therefore  required  to  find  H  in  BC. 

Kence  find  HP,  the  perpendicular  upon  EB-  Area  of  /±  EBh  -  BE  *  ^ 

2 

.'.HP  -  2  x 


BE 

We  now  have  the  angle  HBP,  angle  BPH,  and  angle  PHB  ,  also 
the  perpendicular  HP;  from  these  the  distance  BH  may  be  computed. 
Also  compute  the  angle  3EH,  i.e.,  the  bearing  of  EH.   With  transit 


*  You  will  find  many  examples  of  this  nature  in  text  books  on  sur- 
veying: the  work  of  Gillespie  snd  that  of  Carhart  are  specially  citeo. 


Sleia.    of  Surv.    1A 


18 


Page  5 


or  compass  run  the  line  EH  aad  check  the  falling  of  the  line  on 
®C  oy  measuring  the  distance  KB. 

Note:  If  the  area  of  SAB  is  greater  than  the  required  area 
to  be  cut  off,  construct  the  triangle  EH'B  and  compute  BH'. 

It  ie  sometimes  required  to  run  a  line  perpendicular  to  a 
given  sice  of  a  fielc  as  a  road  skirting  the  side  of  such  field 
and  to  part  off  i^  this  means  a  definite  area.   Suppose  that  a 
certain  number  of  acres  are  to  oe  cut  off  from  the  right  hand 
portion  of  the  field  MNOPR  oy  a  line  perpendicular  to  the  road 
extending  along  MR  (Figure  48). 

0 


'=^_^---^---  Road 


Figure  48 

Erect  the  perpendicular  PS  forming  the  triangle  RSP  and 
having  computed  the  area  deduct  it'  from  the  required  area.   Assume 
a  point  I  and  draw  TX  also  perpendicular  to  MR.   The  area  of  the 
trapezoid  I  SEX,  may  now  be  measured  and  computed.   If  this  area 


Flen.  of  S 


Assignment  i 


differs  from  the  residual  area  as  found  above,  adjust  the  line  TX 
Dy  successive  trials  until  the  small  difference  becomes  less  than 
any  appreciable  quantity.  This  may  oe  done  by  office  computation 
and  the  true  line  run  in  the  field. 

Had  it  been  required  to  run  the  dividing  line  at  a  given 
angle  other  than  perpendicular,  a  trial  line 'might  have  be  en  .\rrom 
a  point,  say,  on  MR  having  the  required  bearing,  the  area  of  the 
part  so  cut  off  computed  and  deducted  from  the  required  area. 
Then  trial  lines  run  at  each  distance  from  the  first  cut-off  line, 
adjusting  the  same  until  the  area  equals  the  residual  area  or 
differs  by  an  inappreoiaole  quantity. 

A  field  having  an  irregular  bounding  line  as  the  meander 
in  Figure  49  is  to  be  divided  by  a  line,  as  KM,  running  from  the 
point  K  and  cutting  off  a  given  area. 

In  this  case  the  survey  of  the  field  should  be  made  to 
include  the  line  BC  and  a  series  of  off-sets  taken  to  the  meander 

line.   Compute  the  area 
of  the  portion  bounded 
by  B£  and  the  meander 
line  and  deduct  this 
value  from  the  required 
area  to  be  cut  off. 

From  K  run  KL  par- 
allel to  BC,  forming 
the  trapezoid  KLBC  and 


Figure  4S 


t  }._•  Page  7 

compute  the  area  of  the  trapezoid  deducting  this  much  also  from 
the  required  area.   The  residual  area  is  now  that  of  the  triangle 
K1.M_;  KL  being  computed  from  the  foregoing,  MP  and  ML  may  be  found 
by  using  the  area  of  the  triangle  KLM  and  the  bearing  of  AB. 

If  the  part  bounded  by  the  straight  line  BC  and  the  meander 
BranopC  be  considered,  it  ie  readily  Been  that  the  area  of  this 
section  is  approximately  the  sum  of  the  areas  of  the  several 
trapezoids  composing  it.   iaicing  the  distances  between  off-sets 
equal  along  BC,  then  BC  (an+bnH-co-fdp)  will  equal  the  area  of  the 
irregular  section. 

(137)       More  accurate  formulae  for  computing  the  areas  of  irregular 
boundary  sections  are 

Area  =  1/2  1  (h^  -f  h£)  for  each  trapezoid,  1  being  a  segment 
along  BC,  and  h^,  hg  being  the  off -sets  at  two  successive  points. 
This  formula  is  known  as  the  Trapezoidal  Rule. 

Simpson's _  1/3  Rule. 

In  this  three  off-sets  at  regular  intervals  are  taken 
and  the  formula  becomes: 

Area  =  1/3  1  (hi  -f  4hg  +  h3). 

Substituting  L  for   2  1  in  the  above  formula  we  have 

L/6   (h,    -e  4hg  •+•  hj)  which   is  the  well   known  Prismoidal 
Formula  applied  to  areas. 

Still  another  formula  known  as  Simpson's  3/8  Rule    is: 
Area  =  3/8   1  (h^  •+  3hg  +  3h3  +  h4). 


Elem.    of  Surv.    1A 


Assignment   18 


page  8 


(138)  CHANGING  BOUNDARY  LINES 

It  is  sometimes  desirable  to  change  the  boundary  or  divis- 
ional lines  of  property,  as  in  Evraight-ening  a  crooked  line  be- 
tween adjoining  properties,  or  placing  a  line  to  alter  the  boundary 
without  changing  the  content.   To  illustrate  this  we  give  a  common 
case  of  the  adjusting  of  the  divisional  line  between  properties, 
the  area  remaining  the  same. 

The  line  oetween  the  property  of  Jones  and  brown  ar  shown 
in  Figure  50  is  to  be  made  straight  by  a  line  starting  at  A  and 
run  in  such  a  vray  as  to  make  no  alteration  in  the  land  area  of 
the  property  of  either  owner. 

A 

The   bearing  snd 
the  distances  of  the  ad- 
jacent  lines,   as  kN,   OP 
and   also  of  A3 ,   bC,   are 
known  and  it  is  first 
required  to  find  the 

bearing   of  the   auxiliary    line  AC.      Then  from  B   run   a   line   parallel 
to  AC    (i.e.,    having  the   same   bearing).      Compute   the   back   bearing 
of  AD  and   run  a   line   from  D  to  A. 

The  triangles  P£,C  end  ADC   are  equal   in   area  having  a  common 
base  AC   of  equal   altitudes   -  the   vertices  3    end  D  falling   on  a 
parallel  to  the   base,      flence   the   line   AD  is  the   line  required.      It 
is    also  .evident  that   the  triangle  AOB    is  equal  in  area  to  COD,  and 
that   by  the   establishment   of   the  new  divisional   line   Jones  receives 
from  Brown  as  much  as  he  yields   by  this  adjustment. 


Elem.  of  Surv.  1A, 


Assignment  18 


Page  9 


QUESTIONS: 

1.  Given  the  following  transit  traverse;  calculate  the  error 
of  closure  and  balance  the  traverse.  Assume  a  reference  meridian 
through  point  A  and  calculate  the  D. M.  D.  of  each  course  from  this 
meridian.  Find  the  area  in  acres. 


Course 

AB 
BC 
CD 
DE 
EF 
FG 
GA 


Bearing 


s 
s 

N 
N 
N 
S 
S 

19° 
44 
22 
60 
8 
69 
88 

33' 
12 
42 
02 
55 
19 
36 

E 
E 
E 
E 
W 

w 

W 

Distance  (feet) 

267.50 
301.89 
266.80 
323.61 
195.65 
354.50 
321.20 


Note:  In  solving  this  proolem  use  the  standard  forms  prepared  by 
th~e"~Department  of  Civil  Engineering.   Submit  original  computations, 
not  a  copy. 

2.   In  the  following  notes  of  a  compass  survey,  the  length 
and  bearing  of  one  of  the  courses  were  omitted.   Supply  the  missing 
data. 


Course 

AB 
BC 
CD 
DA 

REFERENCES: 

Bearing 

N  30°  30'  E 
S  64     20     E 
S  13     15     W 
omitted 

Pages  421  -  427 
163  -   165 
213   -  219 
Hosmer          "        414  -  419, 

Distance   (chains) 

28.37 
34.21 
41.90 
omitted 

Vol.    I 

Tracy 

Raymond 
Johnson 
Breed  & 

- 


Course   1A 


UNIVERSITY  OF  CjuLIFduslA  EXTENSION  DIVISION 
CGrtRESPGtiDMCE  COURSES   IN  BJGINEEKING  SJdJLCTS 

Elements  of  Surveying 
Assignment  19 

SURVEY  OF  THE  PUBLIC   LiNDS. 


(13S)   FOBETNOKD 

In  1785  the  Congress  of  the  United  States  oy  enactment 

decreed  that  th£  public  domain  should  be  divided  by  survey  into 

v 

townships  six  miles  square,  containing  36  sections, each  one  mile 
square.   This  seemingly  simple  plan  carried  with  it  so  many  un- 
looked-for complications,  that  an  elaborate  scheme  was  required 
to  carry  out  the  ideal  conception  of  covering  a  spherical  surface 
with  rectangular  tracts.  We  need  not  follow  the  evolution  of  this 
scheme.   The  purpose  of  the  Assignments  19  and  20  is  to  show  how 
the  present  methods  are  applied  in  Public  Land  Survey. 

In  general,  then,  the  scheme  provides  for  the  laying  out 
of  meridians  and  parallels  of  latitude  primarily  determined  by  an 
initial  point  carefully  chosen  and  established.   The  rectangular 
subdivisions  are  laid  out  to  conform  with  these  primary  lines. 

(140)  INITIAL  POINTS 

Initial  points  from  which  the  lines  of  the  Public  Surveys 
are  to  be  extended  are  established  whenever  necessary  under  di- 
rection of  the  Commissioner  of  the  General  Land  Office.   These 
points  are  selected  with  a  view  to  the  survey  of  extensive  agri- 
cultur&l  areas  within  reasonable  geographical  limitations.   The 
position  of  an  initial  point  in  latitude  and  longitude  is  determined 
by  accurate  field  astronomical  methods. 


Elem.  of  3urv.  1A          Assignment  19  Page  2 

Three  such  points  in  California  are  iit.  Diablo,  long.  121°54'4S", 
lat.  37°51'30";  Humbolot,  long.  124°07'll",  lat.  49°25'04";  San 
dernardine,  long.  116°56'15",  lat.  34007'10".   Suitable  monuments 
marking  these  points  have  been  erected  on  lit.  Diablo,  Bit.  Pierce 
(Huroboldt) ,  and  Mt.  San  Bernardino  as  affording  at  once  a  permanent 
and  prominent  mark  from  which  the  primary  lines  are  extended.* 

(141)  PRINCIPAL  iaERItlAN 

This  line  is  extended  nortn  and  south  through  the  initial 
point  and  conforms  "with,  the  true  meridian.  On  the  principal  mer- 
idian are  set  quarter  section  corners  and  section  corners  at  40 

and  80  chains  respectively,  and  regular  township  corners  at  430 

at 
chains.  Meander  corners  are  set  ail  meaaderable  bodies  of  water, 

as  streams,  lakes,  etc.  Such  meridional  lines  are  rigorously  de- 
termined oy  astromomical  means,  the  line  measurements  are  made 
by  refined  methods,  usually  two  or  more  times  for  check.  Every 
reasonable  effort  is  exercised  to  insure  the  accuracy  of  the 
alignment  and  the  measured  lengths.   If  the  tests  show  a  deviation 
of  3'PO"  or  a  discrepancy  of  more  than  20  links  in  80  chains  (1  mile;, 
then  the  line  is  remeasured  ,to  reduce  the  error  and  also  the  line 
is  changed  in  azimuth  to  reduce  the  error  in  alignrr.ent.   The  es- 
tablishment of  a  Principal  Meridian  oeing  fundamental,  the  precise 
determination  is  essential  as  it  affects  all  surveys  related  to  it. 

2)  BASE  LINE 

I        From  the  initial  point  the  Base  Line  is  extended  east  and 


*  For  a  complete  list  of  Initial  points  see  Manual,  of  Surveying 
Instructions,  Chap.  Ill,  issued  by  the  General  Land  Office,  Wash- 
ington, D.  C. 


Elern.  of  Surv.  1A          Assignment  19  Page  3 

west  on  a  true  parallel  of  latitude.   Upon  this  line,  as  upon  the 
Principal  Meridian,  quarter-section  and  section  corners  are  estab- 
lished at  intervals  of  40  chains  and  80  chains  respectively  and 
standard  township  corners  at  480  chains;  also  meander  corners 
where  the  line  intersects  bodies  of  water. 

A  straight  line  as  projected  through  any  point  in  an  east 
and  west  direction  is  the  arc  of  a  great  circle  of  the  sphere  (the 
earth).   It  will  not  be  coincident  with  a  parallel  of  latitude, 
but  may  be  conceived  as  a  tangent  at  the  c  oioirou  point  from  which 
the  parallel  may  be  run  through  points  determined  by  off-sets. 
This  is  known  as  the  Tangent  Method  of  running  a  parallel.   It 
is  conveniently  used  in  open  country  sparsely  covered  with  forest 
or  underbrush,  where  thicfc  brueh  end  close-set  trees  do  not  inter- 
fere seriously  with  the  measuring  of  off-sets.   If  the  country  is 
not  open,  another  and  more  expeditious  method,  known  as  the  secant 
method,  of  running  parallels  of  latitude  is  employed.   Ihe  secant, 
also  the  arc  or  a  great  circle,  is  run  from  a  point  south  of  the 
initial  point  or  township  corner,  which  is  carefully  determined, 
the  distance  from  the  corner  being  a  function  of  the  latitude. 
The  secant  is  then  projected  east  or  west  as  the  case  may  be.   It 
will  cut  the  parallel  at  the  one  mile  and  five  mile  points  and  off- 
sets will  locate  the  other  mile  points  on  the  parallel.   This  and 
the  tangent  method  will  be  fully  explained  in  Assignment  XX. 

If  meridional  lines  are  accurately  run  at  the  mile  and 
quarter-section  (1/2  mile)  points  and  east  and  west  lines  run  through 


Elem.  of  Surv.  1A          Assignment  19  Page  4 

such  meridians,  a  eeriee  of  such  east  and  west  lines  will  lie 
approximately  in  F.  curve  which  follows  the  parallel  of  latitude 
for  each  point.   To  lay  out  a  parallel  toy  such  method  requires, 
however,  that  meridians  be  established  by  strict  astronomical 
means  and  that  a  small  correction  to  alignment  be  applied  at 
each  mile  point  oa  the  east  or  "west  line.   In  some  cases,  where 
from  the  nr.ture  of  the  territcr^  surveyed,  neither  the  tangent 
nor  the.  secant  method  is  conveniently  applicable,  then  the  "solar 
method11,  as  this  third  method  is  called,  may  "os  preferable. 


(145)  STANDARD  P^ 

These  are  parallels  of  latitude  which  run  in  the  same 
manner  as  the  oase-iine  at  intervals  24  miles  apart,  north  and 
south  of  the  base  line.   The  24  mile  intervals  are  chosen  as 
they  include  4  intervals  of  6  miles  each  which  is  a  dimension 
of  the  township.   Care  is  exercised  in  laying  out  standard  parallels 
as  they  constitute  lines  of  control  in  the  suodivision  Oi  the  24 
mile  tracts  into  townships. 

t)  GUIDE  MERIDIANS 

Guide  meridians  are  extended  north  end  south  from  the  base 
line  e.  t  intervals  of  24  miles  east  and  west  of  the  principal  mer- 
idian.  As  all  meridians  are  not  parallel  lines,  but  converge  to- 
ward the  pole,  they  will  not  intersect  the  standard  parallel  north 
or  south  at  intervals  of  24  miles,  but  the  intersection  cf  the 
guide  meridian  v/ith  the  standard  parallel  is  marked  »nd  such  a 
point  is  named  a  "Closing  township  corner".   Also  in  running  guide 


Llem.  of  Surv.  1A 


Assignment  19 


Page  5 


3rd  Ste 

indard  Par  a  11 

el  North 

16  i 

~~  ;         f 

Toifnsljiips 

~ 

- 

Second 

Standard 

parallel  Nor 

th 

T 

• 

t 

^ 

(a 

f—  2  1  mi  .  *  i^ 

* 

-P 

CS 

-P 

CM 

<0 

M 

to 

First 

Standard 

Parall^ 

North         w 

W 

-P 

to 

q 

c 

to 

£ 

c 

c 

§ 

3 

•H 

d 

<D 

•H 

•H 

•c 

i& 

•4^                                            ^ 

^ 

•0 

•O 

•H 

•H 

wj 

« 

•H 

•H 

h 

L 

£               § 

•H 

•H 

IN 

fe 

i 

i 

Base 

Line          *** 

.H 

C 

i 

i 

•Hi                                         JH 

JS 

r_ 

ft 

•D                                       0) 
•H                                        S 

1 

^Initial 

O 
tf 

& 

SSI                                      (13 

^3 

C3 

•a 

•rt 

P 

•i- 
| 

Point 

03 

.  ts 

1 

•a 

•H 

o 

* 

'3 

Vi* 

0                                  3 
•O                                 Cfl 

First 

Standard 

Parallel   ° 

Soath 

•H 
3                                          TD 

^ 

-P 

"8 

O                                  C 

to 

n 

0 

T3 

o 

4             g 

S,                                    W 
•H 

•rt 

•H 

pr-, 

co 

•H 
g 

X 

E- 

Second 

Standard 

Parallel 

South 

Third 

bland  a  id 

Parallel 

South 

if-  24  mi-.  —  ^ 

Diagram  of  Division   i 
Shovring   Initial  ^oint,   riase 

ito  24  Mile 
Line,    Princi 

Tracts 
pal  Meridiar 

, 

Guide  Meridians,   •  nd 

Standard   parallels 

Figure  51. 


Elem.  of  Surv.  1A 


Assignment  19 


Page  6 


East 


: 

6'^ 
Ife 

4 

3 

2 

1 

/ 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

_ 

xi 
-p 
h 
o 

ss 

i 

19 

20 

21 

22 

23 

24     . 

1 

1 

1 

30 

29 

28 

2? 

26 

25 

30 

31 

,    32 

33 

34 

35 

36 

) 

V 

i) 

f, 

1 

P 

West 


160   120    80 


40 


Diagram  oi'  Township  suodivided 
showing  order  of  numbering  Sections. 


Figure  52 


of  burv.  lA 


Assignment  3.9 


Page  7 


meridians  south  of  any  base  line,  the  linear  convergence  is  set 
off  on  the  base  line  from  computed  values,  thus  causing  the  stand- 
ard parallel  24  railee  south  to  bt  subdivided  into  township  dis- 
tances of  6  miles. 

Where  intervals  of  more  than  24  miles  nave  oeen  established, 
as  in  certain  old  surveys,  a  new  standard  parallel  or  other  guide 
meridians  ine.y  be  run  to  which  a  special  designation  is  given: 
such  as  "auxiliary  parallel";  "Cedar  Creek  Correction  Line"; 
"Auxiliary  Guide  Meridian";  or  "Grass  V&lle;.  Guide  Meridian". 

.145)       The  diagram  of  24  mile  tracts,  Figure  53,  shows  the  Initial 

">» 

Point,  Ease  Line,  Principal  Meridian,  Standard  Parallels,  and 
Guide  Meridians.   These  constitute  the  primary  subdivision  of  the 

Public  Lands.  The  24 
mile  tracts  are  subdi- 

t 

vided  into  townships 
6  wilts  square  and  these 
in  tarn  into  sections 
one  mile  square,  36  sec- 
tions in  each  township. 

The  townships  are 
numbered  in  each  range 
north  and  south,  the 
tiers  of  tov.-nships  con- 


.st  Standard 

1                     -T 

Parallel  North 

1 

1 

JT4K 
fe3E 

'  L  I 
iaeridian  East 

09 

£ 

cT 

s 

•rt 
13 

tSK 

R2W 

§ 

•H 

'd 

•HI 

**! 



fa 

O 

'3 

i 

i3ase 

Line 

u> 
•*T3~ 

t 

•H 

<D 

•-3 

3 

•H 
O 

T2S 

R3W 

i 

i       *-" 

fl~ 

CO 
iH 

fe 

I3S 
'R4E 

n 

f-i 

1st 

Standard 

Parallel  South 

Figure  53 


stituting  ranges.   The 


Elem.  of  Surv.  1A          Assignment  19  Page  8 

ranges  are  designated  as  range  1  east  (R1E)  or  range  3  west  (R3VS) 
etc.  The  township  numbering  is  Twp.2N»R4E,  etc. 

The  survey  of  townships  begins  at  a  corner  on  a  meridional 

line.  The  east  and  west  boundaries  are  surveyed  as  true  meridians, 

and  quarter-section 

and  sect ion .corners  are  established  at  each  80  and  40  chain  inter- 
val.  The  township  corners  are  also  established  at  480  chains  end 
meander  corners  at  meanderable  bodies  of  water.   The  parallel 
boundaries  falling  upon  a  base  line  or  standard  parallel  or  a 
meridional  line  upon  an  estaolished  guide  meridian  or  principal 
meridian  need  not  be  relocated,  but  such  lines  and  locations  must 
be  checked  to  verify  measurement  and  location  by  a  former  surveyor, 
and  if  found  to  be  correct,  they  are  entered  in  the  notes  of  the 
subdivisional  survey. 

(146)       Let  it  be  required  to  subdivide  the  24  mile  tract  immedi- 
ately to  the  north  and  west  of  a  base  line  and  principal  meridian. 
The  surveyor  checks  first  the  principal  meridian,  by  running  one 
mile  or  more  north  from  the  initial  point,  and  then  the  standard 
parallel  (in  this  case  the  baee  line),  by  retracing  the  line  to 
the  west  from  the  initial  point  and  compares  the  bearings  and 
distances  observed  with  those  of  the  original  survey  of  the  24 
tnile  tract.   Ke  then  continues  to  the  southwest  corner  of  town- 
ship 1  range  1  T/eet  (which  is  the  southeast  corner  of  township 
1  range  Z  west)  and  having  set  tip  his  instrument  at  this  corner 
proceeds  to  determine  the  true  meridian  ./hich  constitutes  the 
v/estern  boundary  of  the  first  range  west  and  the  eastern  boundary 


I,4.6i.i.  of  jaiU'.-.  ?.;  Assignment  i.'i  Page  9 

of  the  second  range  west  of  townships.   Proceeding  northward  on 
the  true  .aeridian  he  sets  quarter-section  and  section  corners  at 
40  and  80  chains  respectively  and  at  480  chains  a  tovmship  corner 
(K.W.  cor.  Twp.lK,  Rlfll).   He  then  runs  due  east  on  a  random  line 
a  distance  of  6  miles,  setting  quarter  section  end  section  corners 
at  40  and  80  chains  to  tne  east  ooundary  of  the  range  (in  this 
particular  case,  the  principal  meridian)  and  notes  the  "falling" 
of  the  li.ie.  If  this  cio;s  not  vary  more  than  3 '00"  of  arc  or 
more  than  20  links  per  mile  (80  chains)*,  then  this  shall  be  es- 
tablished as  the  true  line.  But  if  the  error  in  alignment  or  in 
distance  exceeds  such  ratios,  then  from  the  "falling"  he  shall 
compute  the  true  bearing,  and  shall,  starting  from  the  estaolished 
point  on  the  east  Doundar.y  run  back  (westward  on  a  true  parallel) 
setting  permanent  quarter-section  and  section  corners. 

Arrived  at  the  northwest  corner  of  township  1  K,  range  1  W, 
he  proceeds  in  like  manner  to  establish  the  remaining  boundaries 
of  township  ?.  N,  range  1  W,  by  meridian,  random  line,  and  true 
parallel,  and  so  with  each  township  of  range  1  west. 

At  the  north  township  in  each  range  any  discrepancy,  either 
excess  or  deficiency  in  measurement,  shall  be  thrown  in  the  last 
half  of  the  section  and  the  40  chain  station  shall  be  greater  or 
less  than  this  distance  by  the  amount  of  such  discrepancy.   So 
also  the  convergence  of  meridians  shall  be  noted  aid  closing  cor- 
ners set  on  the  standard  parallel  north.   In  running  the  township 


*These  constitute  errors  of  1  in  4000  in  measurement  and  1  in  1800 
in  alignment. 


.i=iii.  or  iarv 


19 


Page  10 


boundaries  of  a  24  mile  trect  south  of  the  case  line,  when  for 
any  reason  it  ie  ceen.ed  :nore  expedient  to  run  from  north  to  south, 
the  amount  of  the  linear  convergence  shall  oe  computed  for  the 
distance  of  2-i  miles  and  the  6  miles  set  off  on  the  base  line, 
x.allowing  for  this  convergence  and  the  meridional  line  run  as  a 
true  meridian  intersecting  the  first  standard  parallel  south  exactly 
at  the  six  mile  point.  Tne  points  set  on  the  base  line  shall  thus 
constitute  the  closing  corners  of  the  24  mile  tract  next  below  the 
oase  line. 

147)       The  subdivision  of  the  township  into  sections  one  mile 
square  is  as  follows  : 

Each  township  is  to  consist  of  56  sections  surveyed  and 
numbered  as  shown  in  Figure  54;  section  one  in  the  northeast  corner 

of  each  and  every  township,  the 
numbering  continuing  to  the  west 
to  include  section  6;  then  sec- 
tions 7  to  12  numbered  toward  the 
east;  13  to  18  toward  the  west, 
and  so.  on  alternately  east  and 
west,  section  56  falling  in  the 
southeast  corner  of  the  township. 


5 

| 

5 

4 

! 
5 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23. 

24 

50 

29 

28 

27 

26 

25 



51 

52 

i 

55 

54 

35 

36 

Figure  54  In  beginning  the  subdivision 

of  any  township,  the  surveyor  sets  up  tne  instrument  at  the  south- 
east corner  of  the  township,  which  is  also  the  s.e.  corner  of  sec- 
tion 36  of  this  toivnship,.  and  runs  north  on  a  true  meridian 


Elem.  of  Surv.  1A          Assignment  19  Page  11 

one  mile,  noting  the  location  of  the  quarter-section  aid  section 
corners  previously  established.   He  then  returns  to  the  southeast 
corner  of  the  township  and  runs  Dy  a  true  parallel  west  as  shown 
by  the  notes  of  the  original  survey  of  the  township  boundary  ob- 
serving the  location  of  the  quarter-section  and  section  corners 
upon  the  parallel,   '.this  brings  him  to  the  southwest  corner  of 
section  36,  which  has  already  been  raonumented  in  the  survey  of 
the  township  exteriors  previously  made.   From  this  point  he  runs 
north  on  a  true  meridian  one  mile  arid  sets  a  permanent  quarter 
section  corner  at  40  chains  and  a  section  corner  at  80  chains 
north  of  the  southwest  corner.  It  is  required  that  both  the 
alignment  and  the  measurement  of  these  stations  shall  be  made 
with  extreme  care  and  the  line  properly  marked  by  blazing  line- 
trees  through  wooded  country;  and  proper  monuments  of  a  permanent 
character  must  be  placed  at  quarter-section  and  section  corners. 
Arrived  at  the  northwest  corner  of  section  36  the  surveyor  then 
proceeds  east  on  a  random  line  in  a  cardinal  direct  ion,  sets  a 
temporary  quarter-section  corner  at  40  chains  on  this  line,  and 
at  the  distance  of  SO  chs.inE  notes  the  "falling"  of  the  random 
with  respect  to  the  east  boundary  of  the  section  and  its  north- 
east corner.   If  this  exceeds  50  links  (1/2  chain)  more  or  less, 
he  computes  the  true  bearing  of  the  line;  starting  at  the  north- 
east corner  of  the  section,  he  corrects  oack  on  the  line;  he  also 
corrects  the  measurement  of  the  quarter-section  (46  chains)  dis- 
tance and  setc  a  permanent  quarter-section  corner  in  its  true 


Elem.  of  Surv.  LA.          Assignment  19  Page  12 

location,  and  thence  proceeds  to  the  northwest  corner  of  the  sec- 
tion, number  36. 

This  is  also  the  southwest  corner  of  section  25  (see  Figure 
54).   From  here  he  proceeds  to  run  the  western  boundary  of  section 
25  on  a  true  meridian,  setting  quarter-section  and  section  corner; 
then  by  random  to  the  cardinal  east  setting  temporary  quarter-sec- 
tion corner,  correcting  back  on  a  computed  true  parallel,  and  es- 
tablishing a  permanent  quarter- sect  ion  corner  as  before  and  arriv- 
ing at  the  northwest  corner  of  eection  25,  which  is  also  the  south- 
west corner  of  section  24.  And  so  ha  continues  to  the  north  tier 
of  sections  tor  to  section  one.   Here  if  the  measurement  northward 
falls  short  or  exceeds  40  chains  on  the  last  half  of  the  measured 
western  ooundary  of  section  one,  then  such  excess  or  deficiency  is 
placed  in  the  last  half  of  such  line  and  the  closing  of  the  line 
on  the  north  parallel  boundary  is  marked  with  a  closing  corner  and 
the  distance  to  the  nearest  corner  on  the  township  north  uoted. 

The  subdivision  is  continued  by  returning  to  the  south 
boundary  of  the  toivnsJr.ip,  and  proceeding  from  here  to  the  south- 
west corner  of  section  35  and  as  before  running  north  on  a  true 
meridian,  ec.st  on  a  random  line,  and  correcting  back  as  before; 
and  so  on  until  the  lest  tier  of  sections  to  the  west  is  reached. 
Here  "having  established  the  west  and  north  boundaries  of  section 
32,  a  random  line  will  be  initiated  at  the  corner  of  sections  29, 
30,  3l>  and  32,  which  will  be  projected  westward  parallel  to  the 
south  boundary  of  the  township  setting  a  temporary  quarter-section 


Elem.  of  Surv.  lA          AE6ig,rini«nt  19  Page  13 

corner  at  40  chains,  to  an  intersection  with  the  west  boundary  of 
the  township,  where  the  falling  will  be  measured  and  the  bearing 
of  the  true  line  calculated,  whereupon  the  line  between  sections 
30  and  31  will  be  permanently  marked  between  the  section  corners 
and  the  quarter-section  corner  thereon  will  be  established  at  40 
chains  from  the  east,  there oy  placing  the  fractional  measurement 
in  the  west  half  mile  as  required  by  law"*. 

The  sections  are  not  subdivided  in  the  field  by  U.S.  sur- 
veyors unless  by  special  provision,  but  certain  subdivisions-of- 
section  lines  are  always  projected  upon  the  maps  (official  plats) 
and  the  local  surveyor  who  may  be  employed  by  entrymen  to  run 
such  lines  in  the  field  is  compelled  to  correlate  the  conditions 
as  found  upon  the  ground  with  those  shown  upon  the  approved  plat. 

The  unit  of  disposal  under  the  general  law  is  the  quarter- 
quarter- sect  ion  of  40  acres;  the  square  mile  (640  acres)  is  the 
unit  of  subdivision;  while  the  unit  of  survey  is  the  township  of 
36  sections  (each  one  square  mile). 

(148)       The  function  of  the  United  States  Surveyor  has  been  ful- 
filled when  he  has  properly  executed  and  monuraented  his  survey 
and  -returned  an  official  record  of  it  in  the  shape  of  complete 
detailed  field  notes  and  a  plat.   The  function  of  the  local  sur- 
veyor begins  when  he  is  employed  as  an  expert  to  identify  the 
lands  which  have  passed  into  private  ownership;  this  may  be  a 


*This  quotation  and  others  to  follow  are  from  the  Manual  of  Sur- 
veying Instructions,  Survey  of  the  Public  Lands. 


Elena,    of  Surv.    lA 


Assignment   19 


Page  14 


simple  or  most  complex  problem,  depending  largely  upon  the  condition 
of  the  original  monuments  as  affected  principally  by  the  lapse  of 
time  since  the  execution  of  the  official  survey.  Also  the  local 
surveyor  must  when  called  upon  be  prepared  to  make  the  suodivisions 
of  section,  to  discover  the  locations  of  "lost  or  obliterated"  cor- 
ners.  To  do  this  effectively  requires  a  full  knowledge  of  the 
methods  of  the  survey,  the  rules  applicable  to  these  matters  as 
laid  down  for  the  practice  of  surveyors,  and  the  rulings  of  courts 
in  certain  cases.   The  suoject  of  "lost  and  obliterated"  corners, 
and  also  the  judicial  functions  of  the  surveyor  will  be  treated 
in  subsequent  assignments. 

PROBLEMS: 


1.     A  uarcel  of  land  is  dsecrioeo  as  north  half  of  the  north- 
east quarter   of  Section  16   in  Tovnsttip  4  North,  Ran^e  3  East,   Mt. 
Diaolo  Base  and  Meridian.      Draw  s  map  shoeing: 

Ihe   initial  poi.it,   b<r.S6,  .meridian,   twenty  four  mile  parallel 
north,   24  mile  guide  meridian  east;   divide   into  townsrips,    subdivide 
the  townships  above   specified,  into  sections  anc   number  thea,    locate 
the  aoove  describee   pe.rcel   in  its  proper  ^1  ct   on  the  map.     Make 
scale   1/4  inch  =  1  mile.     Designate  each  township  by  number  and 
range . 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 
CORRESPONDENCE  COURSES  IN  ENGINEERING  SUBJECTS 


Course  1A  Elements  of  Surveying 

Assignment  20 

SUHVEY  OF  THE  PUBLIC  LANDS  (Cont.) 

FQSBWCRD 

This  assignment,  continuing  the  general  subject  of  "U.  S. 
Public  Land  Survey",  will  explain  Convergence  of  keridians,  the  Tan- 
gent Method  of  running  a  parallel  of  Latitude,  the  Secant  Method 
of  running  a  parallel,  and  Obliterated  or  Lost  Corners.   For  ref- 
erence the  student  is  directed  to  the  Manual  of  Public  Land  Sur- 
vey published  by  the  General  Land  Office,  Washington,  D.C. 
L49)  CONVERGENCE  OF  MERIDIANS 

AE  all  meridians  pass  through  the  Pole  of  the  earth,  any 
two  adjacent  meridians  are  at  maximum  distance  apart  at  the  earth's 
equator  and  approach  each  other  (converge)  until  they  reach  the 
pole  where  the  distance  between  them  is  zero. 

ANGULAR  CON  VEkG  EtiCE  . 

In  Figure  55  let  T  and  I1  be  the  tangents  to  two  given 

meridians  whose  angular  convergence  is  required,  aiSN  being  that 

angle.   Then  if  R  is 
the  mean  radius  of  the 
earth  aud  r  that  of  the 
parallel  of  latitude  MM 
(mean  parallel  of  lati- 
tude under  consideration) 


Angular  Convergence 
Figure  55 


we  have  by  spherical 
trigonometry 


Elem.    of  Surv.    1A  Assignment  20  Page   2 

r  &  R.cos   Lat. 

T  =  R.cot   Lat. 

But   tty   radian  measure  the  arc  MN  subtends   angles   inversely  pro- 
portional to  the  radii  to  this    arc  and  since  MN  (in  circular  units) 
is  the  difference   in  longitude  of  the  two  meridians  we  may  write 

MSN £.   v,ence  MSN  _  K   •    cos   Lat. 

Diff.  in 'Long.  "  I'     "  m   ~  R  •  cot  Lat. 

cos 

=  sin  (trigonometric  relation),  therefore, 

cot 

MSN 

-rrr  -  sin  Lat. ,   and  EiSK  =  M   •    sin  Lat. 

JYl  1M  »— ™^»          _i  _    JT  ^ 

In  other  %vords,  the  angle  of  convergence  of  two  meridians 
in  found  by  multiplying  the  difference  in  longitude  by  the  sine 
of  the  mean  latitude. 

If  the  longitude  it>  given  in  hours,  minutes,  and  seconds, 
this  v>lue  should  be  reduced  to  degrees,  minutes,  and  seconds;  and 
if  the  longitude  is  measured  in  linear  units,  this  should  be  re- 
duced to  angular  measure  by  finding  the  value  of  one  degree  using 
a  value  for  r  (the  radius  of  the  parallel  arc)  from  the  equation 
r  =  R  •  cos  Lat.  While  this  is  not  precisely  correct,  the  mean 
value  R  is  sufficiently  near  for  purposes  of  land  surveying. 

(150)  LINEAR  CGi^VEHGLulCE 

In  practice  the  linear  convergence  is  set  off  in  feet  or 
chains.  This  may  be  determined  from  the  formula  C/l  =  sin  MSN, 
in  which  C  is  the  linear  convergence  1  is  the  distance  on  the 
meridian,  and  MSK  ie  the  kngle  of  convergence.   Ihis  equation 


Elem.  of  burv.  LA          Assignment  20 

reduced  is       C  =  1  •  sin  MSN. 

As  the  meridians  approach  each  other  toward  the  pole,  the 
correction  IE  subtractive  northward,  additive  southward. 

A  principal  meridian  is  always  established  in  the  field 
by  astronomical  me ens,  i.e.,  it  is  a  true  meridian  as  nearly  as 
human  agencies  can  determine.   Meridians  to  the  east  of  the  prin- 
cipal meridian  converge  toward  the  principal  westward;  likewise 
those  to  the  west  converge  toward  the  principal  eastward,   iience 
the  closing  corners  in  the  east  cjuadrar.gle  fall  west  of  fetandard 
corners  in  the  next  quadrangle  north,  and  such  closing  corners  in 
the  west  fall  east  or  their  respective  standard  corners. 

The  linear  convergence  when  determined  for  any  township 
length  of  6  miles  may  be  set  off  1/6,  1/3,  l/£,  2/3,  5/6  at 
each  successive  section  corner^  this  simplifies  computations. 

51)  TANGENT  METHOD  Or  RUNNING  A  PARALLEL  CUhVE 

If  it  is  desired  to  set  out  a  true  latitude  curve  east  (or 
west)  of  a  given  point  the  Tangent  Method  may  be  used  as  follows: 

If  a  line  be  run  due  east  (or  west)  from  any  given  point 
on  the  earth 'e  surface,  such  a  line,  which  is  the  arc  of  a  great 
circle,  departs  from  a  true  parallel  by  an  amount  which  is  a 
function  of  the  latitude.   At  the  equator  the  departure  is  zero, 
the  departure  increasing  as  the  latitude  increases.   This  may  be 
seen  by  observing  that  a  so-called  straight  line  east  or  west  is 
the  arc  of  a  circle  having  the  earth's  center  for  arc  center,  while 


Elem.  of  Sur-v.  1A 


Assignment 


Page  4 


parallels  of  latitude  are  the  circles  formed  oy  planes  parallel 
to  the  equatorial  plane. 

A  line  projected  east  (or  west)  from  any  point  in  a  parallel 
of  latitude  north  of  the  equator  will  depart  ir.ore  and  more  to  the 
south  as  it  is  carried  east  (or  west)  of  the  point.   It  will  be 
tangent  therefore  only  rt  point  of  beginning.   This  straight  line 
is,  hence,  called  the  tangent  am  is  conveniently  mad*  use  of  in 
laying  out  the  parallel  curve. 


\    Latitude 
>  45°34'51"N 


Off -sets  in  Linics 


37 


Figure  56 


By  reference  to  Figure   56  (exaggerated  for  sake  of  clearness) 
the  method  may  be   reedily   followed,   thus : 

Set   un  the-  transit   sna  turn  cff  an  angle   of  90°   and   project 
the  tange.it  a  distance   of   six  miles,   the  nieagureraents   being  c^ae 
i'cr  each  corner  point   at  40,    80,    120,    etc.    chains.      Measure  proper 


Elem.    of  Sarv.    1A  Ai.sitonjnent   20  Page   5 

offsets  north  from  the  tangent  to  the-  parallel,  and  upon  the    latter 
establish  the  corners.      Standard  field   Tables,   prepared   'ay  the  Gen- 
eral Land  Office   and  contained  in  the  kanual ,   give   the   bearing  angles 
and  also  the  off -sets  for  each  mile  from  1  to  5.      The  hall -mile   off- 
sets  should  be  determined   by  interpolation;   the  qj  arter-sectioa 
corners   should   be  checked  accordingly.      The  form  of  record   is  also 
given  in  the  Manual   by    specimen  field  notes. 

The  tangent  method   is   in  favor   in  open  or  untimbered  country. 
In  a  timbered  country  the   blazing  on  the  true   line   and   the  measure- 
ment of  large  off-sets  are  made  with  difficulty;  hence  the  secant 
method   is  used. 

(152)   SECANT  aJ&ItiOD  OF  h'JNNIBG  A  LKTITUDt  CUKVL 

This   is  a  modification  of  the  tangent  method.      Range  out  a 
line  east  (or  west)   for  a  distance   of  six  miles,   cutting  the  true 
parallel   of   latitude  at  the   first  and   fifth  mile  corners   anf 
iorining  a     tangent  to  an  imaginary   latitude  curve   at   the  middle 
mile  point.     Reference  to  Figure  57  will  make  plain  the   bearings 
and   relative  points   of   secant   line    md  parallel  curve,  and  the 
direction   anc?   order   of  the    offsets  required  to  accomplish  the 
purpose. 

A  point   on  the  meridian  south   of   the   township  corner   from 
which  the   parallel   is  to  be  run   is   located   o.y   computing,   the  dis- 
tance  being  e   function  of  the   latitude.      Then  from  the  meridirn 
the  proper   deflection  angle   is   taken  from  taole  prepares  by   the 
General   Land  Office.      Off-sets  are  ;aeasurec   and  corners   established 


Elem.  of  Surv.  1A 


Assignment  20 


Page  6 


SEC  AM 'I  WLIHOD 


Off  -sets  in  links 
Secant 


(5   TT 

1—  ..  i  .  .-.,.!.-    — 


400   440   480 


True  Parallel 

40     30       160      240      32C 
Distances  in  Chains 

Figure  57 


at  every  40  and  80  chains;  these  also  are  tafcen  from  a  table  of  off- 
gets.   It  will  oe  noted  that  the  distances  south  of  the  parallel 
on  the  meridional  lines  east  and  west  are  symmetrical,  that  the 
secant  cuts  the  curve  at  the  first  and  fifth  mile  points,  that 
between  these  two  points  the  parallel  lies  south  of  the  secant 
and  at  the  0  and  6  mile  points  north  of  the  secant.   Furthermore, 
the  off- sets  are  all  short  compared  with  most  off -sets  on  a  tan- 
gent an<5  the  secant,  therefore,  follows  more  nearly  the  line  of 
the  curve;  this  last  fact  renders  the  secant  method  in  some  re- 
spects preferable. 

53)  RESTORATION  OF  LOST  OK  OBLITERATED  C OWNERS 

Perhaps  nothing  in  the  work  of  th3  surveyor  gives  more 
trouble  and  therefore!  cells  for  greater  care  than  the  restoration 
of  lost  aid  obliterated  corners.  The  best  practice  evolved  through 
many  years  and  regulated  by  the  rules  laid  down  by  the  General  Land 


Hero,  of  Surv.  1A          As  ?  igrment  20  Page  7 

Office  and  further  defined  by  many  court  rulings  is  embodied  in  a 
chapter  of  the  instructions  contained  in  the  Manual,  to  which  you 
are  referred.  Some  general  rules  and  principles  may  be  set  forth 
here. 

A  distinction  should  be  made  in  the  use  of  the  terms  "corner" 
and  "monument"  as  follows: 

A  corner  means  a  point  determined  oy  the  surveying  process, 
while  the  term  monument  signifies  the  physical  structure  erected 
to  mark  the  corner  point  upon  the  earth. 

Again,  distinction  is  made  between  lost  and  obliterated 
corners.   If  the  physical  evidence  of  location  of  a  corner  has 
been  removed,  but  the  marking  can  be  restored  upon  adequate  testi- 
mony or  other  available  evidence  the  corner  is  not  lost  out  is 
classed  as  obliterated.  Where  both  the  physical  evidences  and 
the  immediate  means  of  locating  a  corner  are  wanting,  end  lines 
must  be  run  from  other  points  and  measurements  by  distance  and 
angle  taken  to  locate  a  missing  corner,  it  is  classed  as  a  lost 
corner.  A  special  procedure  must,  hence,  be  followed  for  the  res- 
toration. 

Surveys  once  made  and  returned  to  the  Commissioner  by  a 
Surveyor  General  and  thus  made  of  record  in  the  Public  Land  Sur- 
vey, are  fixed  and  immutable  for  all  time.   Therefore,  the  sur- 
veyor has  no  authority  to  fix  any  point  except  Dy  the  means  di- 
rected for  that  purpose.   The  surveyor  then  should  note  the  dif- 
ference between  the  regulations  for  the  original  survey  of  the 


Elem.  of  Sury.  1A          Assignment  20  Page  8 

Public  Lands  and  such  as  relate  to  identification  of  official 
surveys  and  the  replacement  of  missing  monuments  on  such  surveys. 

In  determining  whether  a  corner  is  lost  or  merely  obliterated, 
the  eurve-yor  should  examine  into  each  case  at  every  angle.   The 
search  for  physical  evidences  having  proved  fruitless,  he  may  take 
the  corroborating  testimony  of  witnesses,  who  can  point  out  certain 
reliable  evidences,  as  the  intersect! one  of  walls,  fences,  center 
lines  of  roads,  stumps  of  bearing  tress,  etc.   Nor  should  he  neg- 
lect to  search  for  ouried  evidences,  witness  corners,  and  line 
tre^s  as  supplying  reliable  evidences  of  a  valuable  nature.  When 
all  eiich  evidences  fail  tlie  corner  may  be  classed  as  a  lost  corner. 

L54)  jffiTHODS  OF  RESTORING  LOST  CORNERS 

A  "single  proportionate"  measurement  is  one  made  in  a  single 
direction,  east  and  west,  or  north  and  south,  between  two  deter- 
minate points  on  the  line.   It  consists  in  locating  the  corner  in 
question  a  proportionate  distance  whether  the  true  distance  or  not, 
by  taking  such  proportionate  measurement  for  tht  fractional  distance! 
as  the  whole  measured  distance  is  to  the  whole  record  distance. 

When  the  lost  corner  is  determined  by  measurements  in  two 
directions,  the  "double  proportionate"  method  is  employed.  That 
is,  proportionate  measurements  are  instituted  in  both  directions 
and  should  this  irethod  locate  the  corner  Doth  in  latitude  and 
longitude  the  same  shall  constitute  the  point  required.  If  the 
measurements  should  not  result  in  locating  a  point  in  common, 
then  by  cardinal  off-sets,  in  latitude  and  departure,  the  corner 
shall  be  established. 


Elera.  of  Surv.  1A          Assignment  20  Page  9 

If  measurements  are  taken  upon  a  principal  meridian  or  a 
base  line,  or  upon  an  established  meridional  line  or  parallel  of 
latitude,  the  single  proportionate  method  applies;  out  where  the 
corner  cannot  fulfill  these  conditions,  then  measurements  are 
taken  in  two,  three,  or  four  directions  and  double  proportion 
must  be  resorted  to. 

Double  proportionate  measurement  is  generally  applicable 
to  the  restoration  of  lost  corners  of  four  townships  and  lost  in- 
terior corners  of  four  sections. 

Monuments  north  and  south  should  control  the  latitudinal 
position  of  a  lost  corner,  and  monuments  east  and  west  should  con- 
trol the  longitudinal  position.  Each  identified  original  corner 
should  be  given  a  controlling  weight  inversely  proportional  to 
its  distance  from  the  lost  corner. 

Lost  exterior  section  and  quarter-section  corners  are  re- 
stored by  single  proportionate  measurements  between  the  nearest 
identified  corners  on  opposite  sides  of  the  missing  corner,  north 
and  south  on  a  meridional  line,  or  east  and  west  on  a  latitudinal 
line,  after  the  township  corners  have  be  an  identified  or  relocated. 

Lost  interior  quarter-section  corners  are  to  be  restored  by 
single  proportionate  measurements  between  the  adjoining  section 
corners,  after  the  section  corners  have  been  identified  or  relo- 
cated.  (Note  the  emphasis  on  "after".) 


Elem.  of  Surv.  1A          Assignment  20  Page  10 

Lost  meander  corners,  originally  established  on  a  line 
across  a  mer,nderaole  body  of  -.rater  and  marked  upon  the  oppos.vte 
side  of  it  will  oe  relocated  by  a  single  proporcionate  measurement, 
after  the  section  or  quarter-section  corners  upon  opposite  sides 
of  the  missing  meander  corner  have  been  identified  or  relocated. 

There  are  otaer  provisions  for  the  relocation  of  corners 
and  retrF.ceinent  of  lines  which  are  beyond  th-=  scope  oi  these 
assignments,  and  the  student  must  not  presume  to  follow  the  meager 
directions  he^e  ^ii/en.   Here  we  give  only  thf;  outline  of  controlling, 
principles  rnd  it  is  not  desired  to  cover  these  up  with  a  large 
mass  of  details. 

You  are.  referred  to  the  "Manual  of  Surveying  Instructions" 
and  to  a  brief  treatise  on  "Restoration  of  Lost  and  Obliterated 
Corners"  issued  by  the  Ceneral  Land  Office,  Washington,  D.  C. 

PROBLEMS : 

1.      Whet   is   the  an;:ular  convergence   of  meridians   6  miles 
apart   in   latituoe  4i/'?      The   length  of   1°   of   longitude   in   latitude 
40°    i&   53.U&5  miles. 

What   is  the   linear  convergence   in  links  at  6  miles?     1, 
2,   3,   4,   5,  miles   ? 

The  N.W.    quarter   of  the  ji.W.    quarter   of  a  certain  section 
measured  20.16  chains  by  18.24  chains;  what   is  the  content  in 
acres? 


:.  i    ..*•  CAUtOIOJIA  EXTENSION  DIVISION 

Correspondence  Ccurse 
Course   IB  Element e  of  Surveying  Svrafford 

Assignment  21 
STADIA     SURVEYING 

FOREWORD 

This  assignment   is  designed  to  explain  the  principle  and 
method   of  the  stadia,   the   scope  and   limitations  of  its  uee,  and 
also   the  application  of  stadia  measurements  to  the  various  branches 
of  surveying  -   land,   railroad,    topographical,  etc. 
(166)  The   Stadia 

It.  is   a  rod  marked  with  linear  units  of  measure  which 
may  be  read  afar  off,   and  from  the  measures  thus   obtained  heights 
and  distances  may  oe  computed!.      The  name    "Telemeter"  has   been 
proposed  and   is  occasionally  used  for   stadia;   this     name   (tele  = 
afar,   meter  =  measure)    like  telescope,   telegraph,  telephone,   in- 
deed fits  the  thing  and  describes   its  use,   but  usages  change 
slowly   and   stadia  still  persists   in  the  language   of    surveying. 
57)  Telescope  and  Stadia  -  Hairs 

To  aid    in  reading  the  distant  rod  a  telescope   is  used. 
This   gives   large  range  and  great  definitenese   to  the  distant 
markings  and  characters.     Also  two  fine  wires  or  spider-webs  are 

introduced  at  the  principal  focus  of  the  telescope  and  these  are 

apart 
spsced  at   such  a  distance^that  they  intercept  a  given  interval  on 

the  rod  at  any  given  distance  from  the  center  of  the  telescope. 
It  is  common  practice,   and   for   purposes   of  computation  quite  con- 
venient, to  space  these  stadia   vires   (stadia-hairs)   so  that  an 


ni.    ol    Surv.    1H 


Assignment    21 


Page    2 


interval  of   1  foot  is  intercepted  on  the   image  oi  the  rod  when  the 
latter   is   100  feet  from  the   instrument;    by  the    law  for  similar 
triangles,  at  200  feet  the   interval  would   tie   2  feet;   at  300  feet, 
3  feet;  at    1000  feet,    10  feet;   etc.;   the   lav?  holding,   of  course, 
for  all  distances   snail  or  great. 

Thus,    by  observing  through  a  telescope   furnished  with  these 
stadia-hairs,   directed  upon  a  rod  held  at  some  distant  point,  and 
by  knowing  the  ratio,     of  the  distance  to  the   rod   intercept,  the 
distance  of  the  rod  from  a  point  near  the   observer  may   be  computed. 
(158)  Theory  of  Lenses 

Before  proceeding  further  with  the    subject  of  this  assign- 
ment,  it  is    best  to  explain  briefly  the  phenomena  of  light  passing 
through   the    lenses  of  a   telescope,  as  follows: 


r- 
f 


r 


Figure  58 

t 
rrr  r  r  r  r  are  parallel  ra;ys  oi  light  (the  rays  from  the 

sun,  or  a  star  of  oi  other  very  distant  luminous  point  are  prac- 
tically parallel).   Such  ra^s  passing  through  the  double  convex 
lens,  L,  are  refracted  toward  the  axis  of  the  lens  upon  their 
passage,  and  are  again  refracted  in  passing  through  the  air,  and 
converge  at  F,  the  principal  fccus. 


-~~ ----.-".•- 

V-    F 


tlera.    of  Surv.    IB 


Assignment  21 


Page  3 


f,  and  fg  are  conjugate  foci;  that  is,  light  rays  emanating 
from  f^  are  focused  at  fg,  and  vice  versa. 

If  f^  is  the  measured  distance  from  L  to  the  focus  in  the 

left,  fp  the  distance  of  its  conjugate  focus,  and  F  the  distance 

of  the  principal  focus,  then  by  the  law  of  optics,  —  +  —  =  — 

fl       f2       F 

In  the  following  figure,    let  AB    oe  the  rod    intercept  as 
seen  through  the  telescope   and   included   between  the   stadia-hairs, 
ab  the   image   (inverted   ae  shown),    i  the  stadia-hair   interval,   and 
f     and  fg  the  distance  of  image  and  rod   respectively;  then  by 
geometry: 


Figure  60 
fg   :   f j  ::   AB    :   ab.      Putting  S  for  AB    (the  rod   interval), 

i   for  ab,  the   stadia-hair   interval  and  writing  in  fractional  form, 

f         *? 

we  ha.ve     2  _  _ 

fl       i 

L5.9)  Principles  of  Stadia  Method 

These  are  two:  the  first  being  that  of  the  law  of  proportion 
for  similar  triangles,  which  is  purely  geometric,   ihe  second  is 
the  law  for  conjugate  foci  of  double  convex  lenses. 

1)  When  light  from  an  infinitely  distant  source  falls  upon  a 
convex  lens  the  rays  are  parallel  and  are  focused  on  the  opposite 


Elem.    of  Surv-    IB  Assignment  21  Page  4 

side  at  a  point  called  the   principal   focue,  F.      If  the   light  ema- 
nates  from  a  near   (or  finite)   source,  fg,   the  rays  are  divergent 
and,    by  the   law  of  refraction,   are   in  such  cases   brought  to  a 
focus,  f   ,   that  falls   beyond  the  principal  focus.     Again,   the 
point  f^  may  be   considered  as  the  radiant  point     and  fp  the  focus. 
Hence,   f     and  t*  are  called  conjugate   foci.      The   law  of  optics 
above  alluded  to  may  now  be  stated  as  follows: 


f2       F 


(1) 


Or  in  words  thus:  The  reciprocal  of  the  principal  focal  distance 
(F)  is  equal  to  the  sum  of  the  reciprocals  of  the  distance  of  the 
conjugate  foci,  all  measured  from  the  optical  center  of  the  lens. 

2)  Suppose  now  that  an  interval  upon  the  stadia-rod  is 
imaged   between  the  two  stadia-hairs   situated  at  the    rod's  conju- 
gate  focus.      Lines  drawn  through  the  optical  center    of  the  lens, 
not  being  refracted,  are  therefore   straight   lines,    the   ray  from 
the  upper   end  of  the  rod   interval  A  will  fall  at  a  on  the  lower 
cross-hair  (image   inverted).      AB  r  rod   interval,   ab  .    stadia-hair 
interval. 

Now  call  the  rod   interval  _S,    the  stadia-hair  interval  i, 
and  the  distances  of  the  conjugate  foci,   f ^  and  f?  as  before,   and 
by  geometry  we  have : 

fo          S 

f  I  (2) 

Solve  the  simultaneous  equations  (1;  and  (2)  for  f?,  i.e.  the  dis- 
tance of  the  rod  from  the  objective  end  of  the  telescope,  and  we 


Kleia.    or  Surv.    IB  Assignment  21  Page  5 

find: 

f2  =  y-S  +  F         (3) 

Thus   it  is  seen  that  the  distance  from  the  objective  to  the 
rod   is  made  up  of  two  parts,     F  s ,  which  is  variable  depending 

• 

upon  the  rod  interval,  and  the  focal  distance,  F,  which  is  con- 
stant for  any  given  instrument.  Moreover,  it  is  always  desirable 
to  measure  the  distance  of  the  rod  not  from  the  objective  but  from 
the  center  of  instrument  (i^e.  from  the  vertical  axis).   It  is, 
therefore,  necessary  to  add  another  quantity  which  we  will  call  c, 
the  distance  of  the  center  of  the  instrument  from  the  objective. 
Hence  we  combine  the  quantities  F  and  c,  giving  a  value,  F  +  c, 
which  is  regarded  as  a  constant  for  a  given  instrument,  and  has  a 
range  in  value  of  from  6.75  ft.  to  1.50  ft.,  usually  regarded 
approximately  one  foot. 

The  distance  c  in  instruments  that  have  the  adjustable  ob- 
jective, is  variable,  but  the  error  introduced  thus  is  a  negligible 

quantity.   It  may  always  be  regarded  as  constant,  and  F+c  deter- 

i> 

mined  for  any  instrument  is,  as  also  ±,  in  instruments  having 

fixed  stadia -hairs,  and,  the  principal  focal  length  of  the  ob- 
jective, being  constant,  £  is  a  constant  ratio. 

i 

F 
The  ratio  L  is   determined  by  the  maker,   and  the    interval 

between  the  stadia-hairs  fixed  accordingly.      In   some   instruments 
the  interval  £  is  made  adjustable  and  may  then  be  set  by  the  user 

to  suit  either   a  given  rod   or  a  desired  ratio,  — . 

i 


- 


• 


Eiera.    01    Surv.    IB  Assignment  21  Page  6 

T? 
Although  the   ratio  ~-  is   usually  fixed  by  the  maker  and  the 

quantity  F+c  depends  upon  the  construction  of  the   optical  parts 
of  the  teleecope,    it   is  best,   always,   to  determine  these  constants 
for   any  given  instrument,   and  the  student  is  urged  to   "try  out" 
the   instrument  to  that  end,    in  the  manner  shown  as  follows: 
(160)   To  determine  the  constant  F+c 

With  an  engineer's   scale  measure  the  distance  from  the 
middle  of  the  objective   lens  to  the  reticule  that  carries  the 
stadia-hairs,  when  the  instrument  is  focused  on  a  very  distant 
object,    such  as  a   star,  the  sun,   or  some  other  very  remote  point. 
By  so  focusing  the   instrument,   the  rays  of  light  entering  the 
objective  are  made  practically   parallel  and,    therefore,   the  image 
is  at  the   principal  focus.     This  measured  distance  is  F.      Now  with 
the  instrument  focused  upon  some   object  at  a  mean  distance   of  oo- 
servation  (which  is  ordinarily  about  500  feet  from  the   observer), 
measure   the   distance  from  the  middle  of  the  objective  to  the  ver- 
tical axis  of  the   instrument   (i.e.    the  center  of    the  telescope, 
which  is    the  horizontal  axis   of  the    same).      This   gives  C.     The 
sum  of  these  two  distances,   F+C ,    is  the  constant   required. 

TT> 

51)  To  determine  the   ratio  — 

i 

Set  up  the  transit  on  a  level  stretch  of  600  to  1000  feet. 
By  means  of  markers  placed  at  varying  intervals  establish  ten  or 
more  points  in  a  straight  and  level  line.   Level  the  telescope  so 
that  the  line  of  sight  may  be  truly  horizontal.  With  the  leveling 
rod  and  two  targets  obtain  rod  intervals  for  each  distance  set  off 


Elem.    of  Surv.    IB  Assignment  21  P»Se  7 

by  the  markers    (pins),   setting  the   lower  target  on  the   lower  cross- 
hair and  the  upper  target  on  the  upper  cross-hair  (for  each  dis- 
tance  in  all  cases  the  rod  must  be  plumb).      Measure  the  distance 

of  each  pin  from  the  transit  point;  deduct  the  constant  F-fc,  pre- 

in  each  case 
viously  determined,  as  above,    for  the  measured  distance^(or   better, 

set  off  the  distance  F-fc  in  front  of  the  transit  point  and  take 
all  measures  of  distance  from  this  forward  point).  The  rod  in- 
terval (i.e.  the  distance  between  the  targets)  in  each  case 

F 
divided  into  the  measured  distance  will  give  the  ratio  -j.        The 

V 

average  of  all  these  -r's  is  the  mean  constant  of  the  instrument. 
CAUTION:  Should  any  one  or  more  of  the  determinations  differ  widely 
from  the  general  observed  value,  such  may  be  considered  in  error 

and  of  course  rejected  in  ootaining  the  nearest  mean,  £. 

I' 
For  further  explanation  of  these  methods  see  the  numerical 
examples  at  the  end  of  the  assignment. 
(162)  Inc lined  Sights 

Our  treatment  of  the  matter  of  stadia  measurement  so  far  has 
been  confined  to  such  as  may  be  made  on  level  ground,  in  which 
case  the  horizontal  distance  is  measured  direct.  But  it  is  seldom 
that  this  condition  obtains;  sights  are  taken  to  points  aoove  or 
below  the  level  of  the  instrument.   Such  are  called  inclined  sights, 
and  the  distances  so  measured  must  be  reduced  to  the  horizontal 
for  purposes  of  surveying  and  mapping.   If  the  rod  could  be  inclined 
over  the  point  of  observation  so  that  the  line  of  sight  was  per- 
pendicular to  the  rod  at  that  point,  the  distance  obtained  thus 
from  the  roc-reading  (stadia  interval)  would  express  the  slope 


Ll«n.    or  Surv.    Id 


Assignment   21 


Page   8 


distance,      i'ha  horizontal  distance,    in  that  case,  would  be  the   slope- 
distance  multiplied  into  the  cosine  of  the  angle  of  elevation  (or 
depression).     The  vertical  height   of  the  point   (over  which  the  rod 
•isi  held)  would  also  be  the   slope-distance    into  the  sine  of  the 
angle   of  elevation  (or  depression). 

In  the  following  figure,   the  horizontal   distance  H.D.  is 
required. 


01  v  2 

•i,     f  s    <••<•»; fc 


(F+c)    sin  c< 


^F+c;cos  c 

HD  =  AB  =• 


sin  ex 


H  I. 


cosc   ex 


(F+c)cos 


B 


Figure  61 


Here  j>  is  the  rod-reading,  when  the   line  of  sight   is  directed  to 
the  point  £  on  the   rod  held  vertically  above  the  point  P  on  the 
ground,  the  rod   being  inclined  toward  the    transit,    so  that  the 
line   of  sight   (i.e.    line   of  collimation  of  the  telescope)  will  be 
perpendicular  to   the  rod  ;   this  point  jp  is  also  at  a  distance  above 
P,   equal  to  the  height  of  the  instrument,  H. I.      The   slope-distance 

measured  along  the   line  of  sight  from  the   center  of  the   instrument 

P 
to  p  on  the   rod  is  4—s  *  (F+c)  and  the  horizontal   distance,   A.B., 


m.  of  Surv.  IB         Assignment  21  Page  9 


is  evidently  the   slope-distance  times  the  cosine   of   the  angle   of 
elevation  oC 

Expressed  in  symbols  thus: 

A  B  =  H.D.  =  Qa  +  (F-t-c)  J   cos  o<     (1) 
Likewise  the  difference  in  elevation  of  the  point  P  over 
transit  point  A  is: 

B  P  =  V.H.  =  |  £s  -t-  (F+c)    6inc<     (2) 


Having  the  horizontal  distance,  we  may  find  the  difference 
in  elevation  simply  by  multiplying  by  the  tangent: 

V.H.  =  H.D.  tan  0^=  (  £  s  +  (F+c)  )  cos  o(  •  tan  o< 
(By  trigonometry  sin  «f  =  cos  c<  •  tan  oc  ) 

Of  course  in  all  cases  where  distances  are  taken  on  level 

F 

(horizontal)  sights  the  simple  formula,  _  s  •*•  (F+c)  is  very  con- 
venient and  should  be  used,  both  because  it  minimizes  liability 
to  error  and  because  it  simplifies  computation. 

Also,  it  has  been  proposed  (and  indeed  some  instruments 
have  been  so  constructed)  that  the  stadia-hairs  be  placed  vertical 
to  read  upon  a  rod  held  horizontal  instead  of  being  placed  horizontal 
to  read  on  a  rod  held  upright  but  perpendicular  to  the  line  of  sight. 
But  both  these  methods  are  not  always  convenient  in  practice  and 
the  usual  v.-ay  is  to  hold  the  rod  vertical  over  the  point  and  apply 
the  necessary  reductions  for  obtaining  the  horizontal  distance, 
H.D.  and  vertical  heights,  V.H.  This  calls  lor  a  further  consid- 
eration of  the  method  known  as: 
163 )  Inclined  Sights  with  Rod  Vertical 

In  the  following  figure  let  AB  be  the  horizontal  distance, 


Elem.    of  Surv.    IB 


Assignment  21 


Page   10 


£  equal  the  rod-reading   (on  rod  held  vertical)  AC  =  BD  =  height 
of   instrument    (H.  !.)>  which  is  also  equal   to  the  distance  of  the 
middle   cross-hair  above    the   point  P;   hence  PB   =  DO  =  V.  H.      Like- 
wise F+c,   =3E   shown,   ma^    be   reduced  to   (F+c)   cos  o(  ,    or    (F+c)   sin 
o(    as   required   for  H.  D.    or  V.  H- 


9 


rXf^-" 

\< 

(F+c) 

sin  o< 

M 

I 

•  fe 

)cos 

c< 

D 

i 

1- 

Figure     62. 


It  can   be   shown  that   the   horizontal  distance  AB   -  H.  D.    = 

F  2 

__E   .    cos     o<    +   (F+c)   cos   c<  (3) 

and   that  the   difference   in   elevation 

TJl 

:  V.H.    =  £.  s   .    cos  c<    .    sin  o*    +  (F+c)    sin  o<  (4) 

Thus  two  important  formulas,    for  the  determination  of  the  two 
desired  quantities,   H.D.    and  V.H.    are  here  explicitly  set  forth, 
and  you  should   become  familiar  v/ith  them,   for  frequent  reference 
will  be  made  to  them  in  further  considerations  and   in  computations. 


Elem.  of  Surv.  IB        Assignment  £1  Page  11 

Certain  changes  are  made  in  these  formulas,  3  and  4,  for 
the  purpose  of  simplifying  computation,  and  also  for  the  construc- 
tion of  tables  suitable  for  stadia  reduction.   If  we  examine  the 
products  (Ffc)  sin  o<  and  (FTC)  cos  o»*  and  compare  these  with  the 

p 

values   (F+C)   sinc*cos,o<and  (F-t-c)  cos  «X.  we  find  that,    in  general, 
the  difference   in  value  is  negligible,      iience  the   term  (F-tc)  may 

be  added  to  the  inclined  distance,  - —  ,   and  these   formulas,  become 

i   s 

H.D.    =|  |s  T  (f*o)l   cos2  o<  (5) 

V.H.   =  j£s  T  (FTC)  1    cos     ot.    .    sin  ot    (6) 

which  are  approximate  formulae,  and  are   commonly  employed.     There- 
fore briefly  - 
)  RULES   for  Stadia  Reduction  with  Inclined  Sights 

For  Horizontal  Distance  multiply  the  rod-reading  by  100*,  add 
(F+c),   and  multiply  by  the  cos^  of  the  angle  of  elevation,   o<    . 

§For  Vertical  Height,   multiply  the  rod-reading   by    100*,   add 
(F+c),   and  multiply  by  both  the  cos  and  sin  of  the  angle  of  elevation. 
8. B. Remark.     Having  determined  the  horizontal   distance,   it  is  only 
necessary  to  multiply  this   quantity  by    the  tangent  of  the  angle  of 
elevation  to  get  V.H. 
(165)   Stad ia  Reduction  Tables 

Tables  will   be  found   in  the  manuals  and  texts  usually  re- 
ferred to  -  Johnson,  Breed  and  Hosmer,  Tracy  and  Raymond,  with 
adequate  explanation  for  their  use.      Logarithmic  tables  for  this 

This  is  the  common  ratio  F/i;     if  the  constant  for  the   instrument 
differs  from  this,   use  the  correct  velue   for  F/i   of  the  given 
instrument. 


Elem.    oi   Surv.    IB  Assignment   21  Page   12 

use  have  been  compiled  and  we  would  especially  call  attention  to 
these  of  Prof.  F.  S.  Foote,  Jr.,  University  of  California  Ritali- 
cations  in  Engineering,  Vol.1,  No.  11.  These  tables,  especially 
the  last,  for  those  familiar  v/ith  logarithmic  methods  of  computation, 
reduce  lot,  work  Co  a  minimum  and  save  the  computer  both  time  and 
labor. 

Note.     Among  the  Proolems  to  accompany  this   assignment,   two  illus- 
trative examples  ar<s  -worked  out   in  detail  to  show  the  methods  of 
computing  by  use  of  the   exact  formula   in  one  case,    by  the  approxi- 
mate fo.rmula   in  the   other. 

The  uses  of  the   Stadia  Method  in  land,  topographical,  and 
railroad   surveying,  v:il2    be   explained   in  the  following  assignment. 

References : 

Tracy,  pp.  303  -  308 

Raymond,  pp.  127  -  140 

Johnson,  pp.  224  -  233 

Breed  and  Hosmer,  pp.  188  -  201,  Vol.  I. 


Elem.    of  Surv.    IB  Assignment  21  Page   13 

The  following  data,   arranged,    in  tabular  form  furnish  the 
elements   of  problems   in  finding  the  horizontal  distance  and  vertical 
distance  from  observed  rod-reading  and  vertical  angle. 
Transit  at  M       F/i  =  100.2;     f-^-c  =  1.2 


Sta. 

Aziiiiuth 

Rod 

Vert.    Ang. 

F/i   S  +   (f+c) 

H-  D. 

V-   D. 

A 
B 

107  °4C' 
241°15' 

6.73 
8.67 

3°24' 

16°30' 

675.5 
869.9 

673.1 
799.7 

40.0 
236.9 

COMPOZAIZONS  FOR  STATION  A: 
Approximate     Method 


F/i  S  f  (f+c)  = 


6.73  x  100.2  4-1.2 
674.3  +  1.2 
675.5 


673.1  x  tan  3°  24'  « 
673.1  x  .0594  =  39.98 
V.  D.  =  H.  D.  x  tan 


H.  P. 

log  F/i  S  +  (f+c) 
"  cos  5°24' 
it   »  30241 


2.82963 
9.99923 
S. 99923 
2.82809 


V.D. 

log  f/i   S  •*•  (f+c) 
11     cos  3°  24' 
"     sin  3°  24 » 


2.82963 
9.99923 
8.77310 
1.60196 


K.   D.    =  673.1  =  Ant i log. 


V.   D.   =  39.99 

40.0     =  Antilog. 


Exact  Method 


F/i  S  cos2cx 

log  F/i   (100.2) 
"     S          (6.73) 
log  coscX(3024') 
"      "   (3P241) 


672.0  =  Antilog 

* 
F/i   S  cos  <x  Sin<x 

log  F/i  (100.2) 
"  S  (6.73) 


2.00087 
0.82802 
9.99923 
9.99925 

2.82735  672.0 

1.2 

H.  D.  =  673.2 


£.00087 
0.82802 
9.99923 
8.77510 
1.6012"2 


(fi-c)  Cos  c< 

log   (f-rcj    (1.2)       =  0.07918 
"     coscx>(3c24l)   =  9.99923 

0.07841 

1.2  =  Antilog 


(f+c)  sin  g<^ 

log  (f+c)  (1.2)  =  0.07918 
"  sin  ^ (3°24')=  8.77310 

8.85228 
0.07  =  Antilog 


39.92  =  Antilog 


Elem.    of  Surv.    IB  Assignment  21  Page   14 

59.92 

0.07 
39.99 

V.D.    =  40.0  ft. 

Thus  for  small  vertical  angle  the  V.    D.    is  the  same   by  the 
approximate  and  the  exact  methods.     The  H.   D.   by  the  two  methods 
differs  by  l/10th  of  a  foot,  which  is  within  the   limits   of  accuracy 
for  mapping. 

CCMPUTATIOES  JOE  STJMION  E 
Approx.   Method 

F/i   S  +   (f+c)  -       8.67  x   100.2  -4-1.2         V.  D.    =  H.D.    x  taneo 
=  868.7     +   1.2  =  799.7  x   .2962 

=  869. S  =  236.87 

H.  D.  V.D. 

log  F/iS  +  (f+c)  =  £.93947  .  log  F/iS  +  (f+c)  =  2.93947 

"  cos<*(l6030')  =  9.98174  "  cos  (16°30')  =  9.98174 

"              =  9.98174  "  sin   (16°30')  =  9.45334 

2.90295  2.37455 

H.  D.  =  799.7  =  Antilog.         V.  D.  =  236.9  =  Antilog 


Exact  Method 
F/i  S  -Cos***  (f  +  c)  •  Cos 


log  F/i  (100.2)   r  2.00087  log  (f-fc)  (1.2)     =  0-07918 

"  S  (3.67)      =  0.93802  "  cos  c*f  (I6°30'p  =  9.98174 

"  cos  o<(16°30')=  9.98174  0  06092 
"   "  "^    "    =  9-98174 

2.90237  1.1  =  Antilog 

798.7  =  Antilog  79J'J 

'i  •  * 

H.  D.  =  799.8 
F/i  S-cos  o<r.  sin  o<  (f+c;-  sin  oC 


log,  F/i  (10u.2)   =  2.00087  log  (f+c)  (1.2)    =  0.07918 

"   S  (8.67)      =0.93802  "  sin  oc(16°30')  =  9.45534 

"  cos  Ov(16030')=  9.98174  9.53252 
"   sin  '        =  ' 


2.37397  0.34  =  Antilog 


236.6  =  Antilog  236.6 

0.3 
236.9 


Elea.  of  Surv.  IB 


Assignment  21 


Page  15 


*  The  expression  cos  o<  .  sin  ex  is  equivalent  to  1/2  sin  2  c<  , 
and  is  commonly  put  in  the  latter  form.  When  using  natural  functions 
in  computation,  this  latter  fora  is  of  advantage  as  it  reduces 
operations  to  a  minimum.  But  in  logarithmic  computation  the  log  cos 
and  log  sin  are  found  together  in  the  table  and  it  is  therefore  more 
convenient  to  use  these  than  to  turn  to  the  part  of  the  tables  giving 
sin  2  c<  and  then  also  to  be  obliged  to  join  it  with  the  colog- 
2  (log  1/2). 

P  R  0  B  L  E  M 


Given  the  following  data : 


-  =   102.4,   F  +  C  =  1.12,  B.M.    107.54  ft. 


Sta. 

Sight 

B.  S. 

H.I. 

F.S. 

North 

ixzim. 

Rod 

Vert 

H.D. 

V.H. 

! 

Elevation 

X 

B.    M. 

4.89 

107.54  Ft. 

A 

6.83 

A 

B 

17023' 

234.5 

7°50' 

C 

152°17' 

452.7 

10°35' 

1 

Determine  the  horizontal  distance,  A  -B,  B  -  C,  C  -  A;  also 
Vertical  Height  above  A,  of  B ,  C,  and  the  elevation  above  datum  of 
A,  B,  and  C.  Also  find  the  interior  angles  of  the  triangle  ABC, 
and  the  azimuth  (from  the  North)  of  B  -  C.   Sketch  the  triangle 
and  place  the  above  determined  values  appropriately  upon  the  sketch. 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 

Correspondence  Course 
Course  IB  Elements  of  Surveying  Stafford 

Assignment   22 
STADIA  SURVEYING  -   STADIA  DEDUCTIONS 

Foreword  :- 

This  assignment  will  treat  of  the  method  of  the  stadia  as 
applied  to  land,  railroad,  and  topographic  surveying,  and  the  use 
of  stadia  reduction  tables  and  diagrams. 
36)  In  General. 

The  stadia  method  of  measuring  distances,  both  horizontal 
and  in  elevation,  is  applicable  within  certain  limitations,  to  all 
kinds  of  surveying  and  furnishes  a  rapid  and  convenient  means  of 
accomplishing  the  work.   In  open  country  where  lines  need  not  be 
cleared  of  growth  that  obstructs  the  line  of  sight,  two  operators 
only  are  required;  however,  an  alert  transitman  may  keep  two  or 
several  rod-men  Dusy  selecting  points  and  giving  red.  If  the  se- 
lection of  points,  as  in  topographic  details,  or  for  locating  con- 
tours, is  to  be  made  by  the  red -man,  he  should  be  intelligent,  quick 
to  discern  the  salient  features  sought,  and  fully  versed  in  the  work 
in  hand.  Otherwise  he  must  act  wholly  under  direction  of  the  in- 
strument man,  who  designates  the  points  to  be  occupied  Dy  the  rod- 
man  as  the  work  progresses.  Where  the  survey  is  over  a  specified 
traverse  previously  determined  or  staked  off,  the  rodman  goes  from 
point  to  point. 


Elem.  of  Surv.  lb        Assignment  22  Page  2. 

(167)  Stadia  Rods 

These  vary  in  style  and  scale  of  graduation  in  accordance 
•with  the  work  in  hand.  The  ordinary  level-rod  is  convenient  where 

»    readings  are  desired  in  feet  and  fractions;  and  for  long  sights, 
a  target  (or  better  two  targets)  may  be  employed  to  advantage.   If 

the  constants  of  the  instrument,  £  and  f+c, have  been  carefully  de- 

i 

terrained,   there   is  little  difficulty    in  making  computations  for 
H-D. "s  and  V.D. 's  from  readings  taken  with  the   ordinary  level-rod. 

(168)  Speaking  Rods 

These  are  especially  convenient  over  short  distances  ranging 
up  to  1000  feet  and  are  carefully  designed  and  marked  to  assist  in 
quick  and  accurate  reading  through  the  telescope.   Such  rods  may 
be  graduated  in  feet  and  decimals;  the  tenths  being  explicitly 
marked  and  the  hundredths  being  read  by  estimation.  The  v»hole  foot 
mark  and  the  0.5  ft.  division  are  also  specially  indicated  to  fa- 
cilitate reading  and  to  avoid  confusing  these  points.  Furthermore, 
for  like  reasons,  the  numbering  of  the  full  foot-marks  is  also  de- 
signed to  avoid  mistakes,  so  the  ^  is  made  of  the  shape  here  given, 
rather  than  thus, 3  ,  which  at  long  range  may  be  mistaken  for  8; 
a  Roman  Vis  employed  instead  of  _5,  and  X  for  10.  Caution  should 
be  exercised  in  reading  6^  for  j),  or  vice  versa,  when  sighting  with 
an  inverting  telescope.   In  the  last  case,  it  is  best  to  observe 
whether  the  number  read  is  near  the  V  or  the  X;  if  the  former,  it 
is  £;  if  the  latter,  it  is  j).   The  illustration  on  the  following 
page  shows  a  good  form  of  speaking  rod.   These  may  be  had  from 
manufacturers  in  a  great  variety  of  designs;  or  the  engineer  may 
devise  a  pattern  for  his  own  use  to  suit  his  own  ideas. 


Elora.    of  Surv.    IB 


Assignment  22 


Page   3. 


9"  ' 


8 


•7 


(169)  Stadia  Rods  are  sometimes  graduated  to  suit  a 
given  stadia-hair  interval;   this  may  be  accomplished 
by  staking  off  a  stadia  course   on  level  ground  with 
stations  at  100,   200,    etc.,  up  to  1000  feet,   and  locating 
the  rod  intervals  as  viewed   through  the   telescope  by  the 
fine  pencil  linea  drawn  upon  the  rod.     wote  that  F  +  C 
should  be  carefully  determined  and   set   off  from  the 
plumb-line   of  the  transit  to  the  zero  station  of  the 
course.      In  general    it  is  better  to  employ  a  rod  gradu- 
ated  in  feet  and  decimals,   as   such  a  rod  may  be  used 

F 
with  any  telescope   of  which  the  constant  ~  has  been 

accurately  determined. 

(170)  For  reading  rod  intervals  at    long  distances  or 
when,   for"  any   reason,   the  whole  interval  is  not   visible 
or  distinct,   the    semi-interval  may  be  ooserved;  twice 

Pig-    63         such  a  reading  is  then  the  rod-reading.     This  requires 
that  a  middle  cross-hair,    (such  as  found   in  most  instruments) 
shall  be  exactly  midway  between  the   upper  and  lower  stadia-hairs. 
To  avoid  mistakes   in  reading  the  rod,   it   is   sometimes  expedient 
to  read   both  the    semi-intervals  and  check  *he  sum  of  such  double 
readings  also   by  observing  the   full  interval.     At  another  time 
the    lower   interval  may  not  read  correctly  owing  to  unequal  atmos- 
pheric  refraction  in    the  lower    strata  of  the  air.     Then  the  upper 
interval   should  be  relied  upon  as  the  more  nearly  correct  means. 
)  Surveying  by  stadia  over  country   oroken  by  hills  and  ravines 

is  not  only  expeditious,    but  usually   is  more  precise  than  measuring 


-V 


Elem.  of  Surv.  lii          AS  signal  en  c,  22  Page  4 

distances  by  ch-in  or  tape.   When  greater  precision  is  required 
than  can  DC  secured  by  stadia  methods,  resort  may  be  had  to  the  . 
nore  accurate  method  by  triangulation  for  principal  lines  and  for 
control,  and  minor  details  requiring  less  degree  of  accuracy  can 
then  be  filled  in  oy  stadia. 

Very  long  lines  greater  than  the  range  of  the  instrument, 
say  lines  of  1500  to  2000  feet  in  length,  may  conveniently  be  meas- 
ured by  "balancing  in"  the  transit  at  an  intermediate  point  in  the 
line  and  sighting  the  rod  in  both  directions;  in  other  words,  by 
measuring  the  line  in  two  segments.  When  doing  this  the  constant 
F  +  c  enters  into  both  segments.   The  device  of  "balancing  in"  in 
this  manner  is  especially  applicable  in  case  an  intervening  hill 
prevents  viewing  the  further  point;  on  such  an  occasion  station 
the  transit  upon  the  elevated  position  on  line  and  take  readings 
as  before  in  both  directions. 
(172)  Traversing  by  Stadia. 

In  this  work  it  must  be  rememDered  that  three  things  are 
necessary  to  be  done.   (1)  The  angular  relation  of  the  lines  in  a 
horizontal  plane  must  be  determined;   (2)  The  rod-reading  must  be 
taken;   (3j  The  angle  of  elevation  must  be  measured.   And  a  fourth  - 
the  magnetic  bearing  is  valuable  as  a  check  and  it  is  recommended 
that  it  should  be  obssrx'ed  to  that  end,  occasionally,  at  least. 

Of  course,  aay  of  the  methods  of  measuring  horizontal  angles 
•with  their  appropriate  checks  may  be  used,  but  the  method  by  azi- 
muths is  generally  preferable;  this  is  especially  true  when  mapping 
is  to  follow,  particularly  topographic  mapping  with  many  details. 


Elem.  of  Surv.  IB          Assignment  22  Page  5 

It  is  important  that  the  angle  of  elevation  be  correctly 
determined;  hence  the  line  of  sight  of  the  telescope  must  be  di- 
rected to  a  point  on  the  rod  as  muoh  above  the  ground  point  as  the 
horizontal  axis  of  the  telescope  is  above  the  point  on  ground  over 
•which  the  transit  is  set.   This  distance  is  called  H.  I.  (height 

of  instrument)  and  is  obtained  by  actually  measuring  the  interval 
from  the  ground  to  the  center  of  the  trunnion  of  the  horizontal 

axis.  For  this  purpose  the  instrument  man  usually  carries  a  short 
tape  and  measures  the  H.I.  at  each  setting.   Some  require  that  the 
rodman  shall  take  this  interval  by  means  of  the  rod  set  up  next 
the  instrument  before  going  to  the  point  to  be  observed  upon  and 
then  setting  a  target  or  other  marker  at  this  height  upon  the  rod. 
However,  the  tape  is  more  convenient  and  obviates  the  necessity  of 
the  rodman  running  to  and  fro  for  this  purpose.  A  ruboer  band  or 
string  passed  around  the  rod  at  H.  I.  serves  well  in  place  of  a 
target;  on  speaking- rods  the  target  is  wanting. 

The  best  way  for  sighting  the  rod  is  to  Disect  the  H.  I.  on 
the  rod  with  the  middle  cross-hair;  then  set  the  lower  stadia  hair 
on  the  nearest  full  foot-mark;  read  the  rod  interval  es  given  by 
both  stadia-hairs,  if  possible;  then,  having  recorded  the  rod 
reading,  again  bisect  the  H.  I.  with  the  middle  cross-hair  and, 
while  the  rod-man  is  going  to  the  next  point,  take  the  reading  of 
the  vertical  arc,  i.e.  read  and  record  the  vertical  angle.  Also 
read  and  record  the  horizontal  angle. 

(The  deflection  angle,  azimuth,  or  bearing,  as 
the  case  requires.)  The  needle  having  been  lowered,  also  observe 


Elem.    of   Surv.    IB 


Assignment  22 


Page  6 


and  record  the  magnetic  bearing.   Notes  for  recording  should  take 
the  following  form: 


TAKEN  IN  FIELD 

OFFICE  COMPUTATIONS 

Inst.  at 

Sight 

Azimuth 

Mag.  Bear. 

Rod 

Vert. 
Angle 

H.  D. 

V.  H. 

Elev. 

Sta. 

H.I. 

A 

4.5 

B 

123°16' 

N  56°45'  W 

4.32 

8°12' 

F 

331°50' 

S  28°1G'  I 

6.45 

4°08' 

(173)       In  traversing,  the  distances,  horizontal  angles,  etc.,  should 
be  observed  both  to  the  forward  station  and  to  the  rear  station. 
The  readings  at  all  stations  throughout  the  traverse  should  be  thus 
checked.   Either  the  azimuth  or  back-azimuth  of  rear  stations  may 
be  recorded.   In  the  above  notes  the  forward  azimuth  of  A  from  F 
may  readily  be  obtained  by  subtracting  180°  from  that  recorded 
aoove  (331°50'  -  180°00'  =  151°50').   So  also,  if  the  zero  azimuth 
is  taken  as  magnetic  south,  then  magnetic  bearing  of  AB  checks 
•within  one  minute  with  the  azimuth,  and  the  magnetic  back-oearing 
of  A^  likewise  checks  the  azimuth  of  the  line.   These  estimations 
should  be  made  a  pr.rt  of  the  field  work,  checking  observed  values 
as  the  work  proceeds.  Computation  of  H.D  's,  V.D. 's  and  elevations 
are  essentially  office  labors  and  are  rarely  carried  out  in  the 
field. 
(174)       In  taking  measurements  for  topographical  data  the  stadia 

possesses  many  advantages  surpassing  most  other  methods  by  reason 
of  the  rapidity  and  the  lesser  cost  in  time  and  labor  required  for 
a  given  amount  of  work.   To  get  the  topographical  details  over  any 

*  Back  azimuth  (-azimuth  +  180°) 
**  Back  bearing  (Forward  bearing, FA,  is  N  28°10'  W) 


Elera.  of  Surv.  IB         Assignment  22  Page  7. 

district  by  transit  and  tape  or  to  get  them  where  differences  in 
elevation  would  be  obtained  by  use  of  the  engineer's  lead,  for 
example,  it  requires  two  parties,  a  transit  party  consisting  of 
an  instrument  man  and  two  chairmen  who  might  also  act  as  flagmen, 
and  for  the  level  party  an  instrument  man  and  a  rodman.  These 
two  parties  would  be  obliged  to  work  over  the  same  territory,  or 
one  set  of  men  working  in  two  distinct  organizations.  But  by 
stadia  one  instrument  man  and  a  single  rod  man  (or  two  or  more  rod 
men  can  sometimes  be  employed  to  advantage)  can  obtain  all  neces- 
sary data  in  equal  or  shorter  time. 

For  purposes  of  control  either  a  triangulation  system  or  a 
carefully  determined  traverse  should  first  be  laid  out  -  this  for 
horizontal  control ;  while  a  series  of  bench  marks  should  likewise 
be  established,  the  same  being  connected  with  a  suitable  datum  for 
a  vertical  control.   The  triangulation  system  or  the  traverse  with 
the  bench  marks  thus  constitute  a  skeleton  or  frame-work  to  which 
the  topographic  details  are  related  and  to  which  they  are  joined 
as  the  work  proceeds.   The  subject  of  Topographic  Surveying  will 
be  treated  in  subsequent  assignments  -  32  and  33  of  this  course. 
But  allusion  is  here  made  to  the  suoject  to  eet  forth  the  possiole 
advantage  with  which  stadia  methods  may  be  applied  in  this  sort 
of  work. 

The  very  skeleton  in  framework,  be  it  triangulation  or 
traverse,  may  oe  determined  in  the  first  place  by  stadia  measure- 
ment.  Such  work,  however,  should  be  done  with  utmost  care,  double 
readings  by  stadia  should  be  taken  on  all  lines  and  observations 


Elem.    of  Surv.    IB  Assignment  22  Page  8 

on  bench  marks,  the^    should  perhaps  be  done  by  means  of  the   level 
on  transit  telescope,   and  made  closely  within  the  precision  limits 
of   such   leveling. 

References  : 

Tracy,   pp.    308-310 

Raymond,   pp.    249,250. 

Johnson,   pp.    233-235 

Breed  &  Hosmer,   p.    168,   Vol.   II. 

PROBLEM 

Compute  the  H.D.,  V-H.  ,  and  Llev  in  the  tabulated  notes 

F 
on  page  6  of  this  assignment.  -.-  •=  100.2;  F  ^  c  =  1.2  ft. 


UNIVERSITY  OF  CA!  IFORNIA  EXTENSION  DIVISION 

Correspondence  Course 
Course  18  Elements  of  Surveying  Stafford 

Assignment  23 


PROFILE.  lEVLLiag  -  CONTOURS  -  GRADE  LIMES 

Foreword. 

While  the  method  of  running  profiles  has  already  been  given 
(see  assignment  8),  certain  observations  respecting  profiles  are 
made  in  the  present  assignment.  We  shall  also  treat  here  of 
contours  and  grade  lines  as  related  to  leveling. 

(175)  When  one  is  surveying  for  profile,  it  is  of  prime  importance 
that  one  should  select  a  well  defined  bench  mark  related  to  a  datum 
of  permanent  character  and  connect  these  distinctly  with  the  profile 
data. 

Datum  should  Qe  either  mean  sea  level  or  some  other  reference 
plane  wisely  chossn.   If  the  survey  is  near  the  eea-Doard  or  some 
government  survey,  a  bench  mark  connected  with  the  survey  may 
readily  be  found.   Other  bench  marks  may  also  be  established  for 
purposes  of  convenience  as  the  survey  progresses  by  differential 
leveling.  The  bench  marks  should  be  as  carefully  selected  as  the 
datum  plane.   Their  description  and  location  should  be  well  defined 
so  that  they  may  be  readily  found  when  required. 

(176)  The  selection  of  suitable  turning  points  is  of  prime  con- 
sideration. These  should  be  chosen  because  of  their  importance 
in  carrying  forward  the  line  of  levels  run  from  bench  mark  to 
bench  mark.   Since  the  readings  on  turning  points  (and  also  on 


Elern.  of  3urv.  IB         Assignment  23  Page  2 

bench  marks)  are  always  given  to  the  one-hundredth  of  a  foot  and 
often  to  the  thousandth  of  a  foot,  turning  points  must  be  selected 
\vith  careful  regard  to  stability,  convenience,  and,  where  they 
are  also  utilized  as  bench  marks,  with  regard  also  to  their  per- 
manency for  such  purpose.   A  turning  point  should  be  constructed 
which  has  the  above  naced  qualities  and  also  which  offers  a  pro- 
jection of  suitable  shape  so  that  the  rod  held  upon  it  will  in 
all  positions  be  at  the  same  elevation.   For  such  a  turning  point, 
a  spike  or  steel  pin  with  a  rounded  head  driven  into  firm  earth, 
the  top  of  a  manhole  cover,  the  higher  edge  of  a  stone  coping,  a 
door  sill  or  curb  stone,  a  railroad  tie  or  rail  may  be  used  to 
advantage.   In  lieu  of  such  artificial  points  many  natural  ones 
suggest  themselves  and  may  often  be  found  in  the  route  of  a  line 
of  levels;  for  exa.npli,  outcropping  rocks,  stones  that  are  firmly 
imbedded,  especially  Qculders,  the  projecting  root  of  a  tree,  a 
stump,  or  a  mark  upon  the  trunk  of  a  tree,  etc. 

If  a  turning  point  is  desired  as  a  bench  mark,  it  is  well 
to  look  to  the  matter  of  permanency,  its  description,  and  avail- 
ability before  adopting  it  for  this  capac.ity. 

In  any  case  where  a  turning  point  is  to  bs  estaolished, 
care  must  be  taiten  to  read  the  rod  to  the  proper  degree  of  accur- 
acy, since  all  subsequent  readings  of  rod  on  the  line  and  in 
fact  the  "Backsight"  reading  on  the  X.  P.  will  affect  the  line 
readings  from  there  on.  Moreover,  the  "foresight"  reading  on  a 
T.  P.  must  be  made  Dsfore  the  level  has  been  disturbed  in  its  last 
setting  and  when  the  instrument  is  in  station  adjustment,  the  bubble 


Elen.    of  Surv.    IB  Assignment   £5  Page   3 

being  precisely  at  center.      Remember  too,    that  the   level   set-up 
in  accurate  ;vork  is  equidistant   from  t\vo   successive   I.    P.  's   in 
order  that  any  error  in  adjustment  may   be  eliminated. 

You  should  choose  points  for    stationing  the   instrument, 
\vhere   stations  are  not  otherwise  provided  by  the    survey,    50  that 

the   level  may   be  used  advantageously  for  taking  the    "backsight" 

and 
reading,    if  possible,   so  as  to   include   several   foresight   readings. 

It  will  be   seen  then  that  a   level   station  (location  of  instrument; 
will   rarely   or  never   ue  upon  tiie   line  of   levels,   but  rather  at  a 
convenient  place  to  one   side;   if  at  a  station  higher  than  the  turn- 
ing point,  not   so  far  aside  as  to  exceed  the  limit   of    "long  rod"; 
if  at  a  station  lower  than  the  T.    P.    certainly  not   so   lov  that  the 
line   of  sight  cuts  the  ground   below  the  foot  of  the   rod.      In  the 
choosing  of  instrument   stations  the   level  man  must   be  guided   Dy 
experience  and  ,5000   judgment.      A  level  plane  may    be   swept   out  by 
the  eye,   the  angle   of   slope  may   aseist   in  judging.     When  the   in- 
strument  is   set  up  at  any  place,    it    should  be   approximately   leveled 
according  to  a   sight  taken  along  the  barrel   of  the  telescope. 
Apart   from  these  things,     a  man's  experience   determines  the  ease 
and   rapidity  with  which  he  m&y  v;orlc.      Be   alert  and   observant;   get 
a  low  point  on  backsight  reacing  where  the  grade   is  falling  and  a 
high  backsight  v;here  the  grade  is  rising  -  these  enable  a  longer 
range   of  foresight   in  either  case. 
(178)  Grade  Line 

The   line  which  marks  the  slope    of  a  road,    railroad,    or 
mine  tunnel,    ditch,   etc.    is  called  the  grade-line.      Such  a   line    is 


Elem.  of  aurv.  IB          Assignment  23  Page  4 

usually  shewn  in  its  relation  to  a  profile  and  is  graphically 
represented  on  the  mapped  profile  for  convenience  and  study  -  and 
also  for  determining  relations  between  the  ground  surface  (profile) 
and  the  finished  road-bed  at  any  point  along  the  line  of  road. 
Grade  lines  are  sometimes  expressed  in  degree  of  angle  of  slope 
(up  or  down)  or  by  precent  of  grade.  We  say,  for  example,  that 
the  grade  has  a  slope  of  1/2°  or  2°,  5°,  etc.,  meaning  that  the 
slope  is  at  the  designated  angle  to  the  hori2ontal  plane  (the 
horizon).  Commonly,  we  say  that  the  grade  is  a  3%,  a  5%  or  0. 2% 

grade.   This  last  means  that  it  rises  lor  falls)  3  feet  in  ele- 
vation at  distance  of  100  feet,  5  feet  in  elevation  at  100  feet, 

0.2  feet  in  100  feet  (for  the  above  grades)  and  so  on. 

To  represent  graphically  a  grade  line,  a  point  is  chosen, 
preferable  at  a  convenient  bench  mark  or  at  the  station  beginning 
any  profile,  and  the  elevation  of  the  grade  line  is  located  then 
at  100  feet  distant  (by  scale);  the  heights  of  the  grade  line  is 
increased  (or  diminished)  by  the  per  cent  amount;  next  a  straight 
line  is  drawn  through  these  two  points.   Should  the  grade  change 
in  degree  (or  percent;,  the  point  at  which  such  a  change  takes 
place  must  be  located  upon  the  line  (as  graphed)  and  the  change 
shown.   The  illustration,  Figure  64,  shows  a  profile  with  hori- 
zontal distances  (stations;  on  a  ecale  of  1  in.  =  60  feet,  and 
vertical  heights  (elevations)  on  a  scale  of  1  in.  =  6  feet.   The 
grade  lines  AB ,  BC,  CD,  indicate  changes  of  grade  along  the  route. 

The  height  of  the  surface  above  grade  line  (or  depth  below) 
may  be  scaled  off  the  profile  chart  at  any  point  along  the  line. 


Elem.  of  Surv.  IB         Assignment  23  Page  5 

Thus,  at  station  0  +  64.,  the  height  above  grade  is  2.3  ft.,  at 
1  +  80  it  is  3.1  ft. ,  at  2  +  40  it  is  4.2,  etc. 

This  relation  of  grade  line  to  profile  will  be  further  applied 
in  crose-section  work,  Assignment  24. 
(179)  Contours 

As  differences  in  elevation  along  a  line  are  graphically 
shown  by  a  profile,  so  the  differences  of  deviation  over  a  ground 
surface  are  represented  by  contours. 

A  contour  line,  or  simply  a  "contour",  is  the  line  showing 
the  intersection  of  a  horizontal  plane  with  the  ground  surface;  it 
may  be  defined  also  as  a  line  of  equal  elevation  over  any  area. 

A  clear  conception  of  contours  may  be  gained  by  conceiving 
an  area  consisting  of  a  depression  of  considerable  extent  filled 
with  water.   Suppose  now  that  the  shore  line  of  the  water  (as  a 
lake)  to  be  marked  upon  the  map;  this  is  the  representation  of  the 
lake  in  plan  upon  a  plane;  the  shore  line  is  a  contour  at  surface 
level  of  the  land  area  surrounding  the  lake.  Now  imagine  that  the 
water  in  the  lake  subsides,  say  one  foot;  the  new  shore  line  will 
mark  another  contour  upon  the  map,  and  so  on;  for  each  subsidence 
the  shore  line  will  determine  another  contour. 

In  case  elevated  portions  of  land  are  present  within  the 
limits  of  the  subsiding  lake,  these  elevated  parts  will  appear  as 
islands  which  rise  higher  and  higher  as  the  water  falls;  the  con- 
tours of  such  high  spots  might  be  shown  by  ring-liKe  lines  encir- 

land 
cling  the  rising^portions  at  various  depths. 


Elem.    of  3urv.    IB 


Assignment  23 


Page  6 


It  v;ill  be  seen  that  lines  forming  closed  curves  may  repre- 
sent the  points  of  equal  elevation  in  depressions  and  upon  peaks. 
Again  let  us  choose  a  given  elevation  in  the  sloping  side  of  a 


Figure   65 

valley,    at  the   lowest   part  of  which  we  will    suppose  a  stream  flows. 
Keeping  our  feet   on  that   elevation  while  we  walk  in  the  up-stream 
direction,  we   shall  find  that  ive  approach  nearer  and  nearer  to  the 
stream;   at  a  certain  point   (where  the  elevation  assumed  equals  that 
of  the  water   in  the  stream,    or  of  the  banks  on  either  side)  we 
cross  over  to  the   opposite   side.      It  must  be  kept    in  mind  that  we 
are  following  a  path  that   is  always  at  the  same   elevation  a  Dove 
some   assumed  datum. 

This   line  may    be   expressed  grapnically  by   a  contour    line 
along  a   stream  as   shown  in  Fig.    66.      The  contours  there  represented 
show  the  540,   545,  and   550  foot  contours  along  the  stream  as  we  go 


Elem.    of   Surv.    IB 


Assignment   23 


Page  7 


up  on  one   side,   cross  the   stream  at  the  given  elevation,   and  return 
on  the   other  side   of  the   valley. 


Figure  66 

Over   ridges  or  around  hills  the  contours  are   shown  as  in 
Fig-    67.      The  dotted   line  indicates  the  back  of  the   ridge;  the 
contours   supposed  to  be  all  at  the  same    interval  are  more   or    less 
evenly  spaced,   at  varying  intervals;   this  shows  that  the  hill 


Figure   67 

(as  here  represented)   has  different  slopes  at   several  points. 
The  contours  over  hills  are  drawn  at  right  angles  to  the  ridges. 
It  will  now  oe  well   to  call  attention  to  the  characteristics  of 
contours   in  the   following  summary. 


Elem.  of  Surv.  IB          Assignment  23  •Page  8 

(180)  Characteristics  of  Contours. 

On  any  contour  the  points  are  at  equal  elevation. 

Every  contour  will  form  a  closed  curve  more  or  less  irregular 
if  the  area  is  of  sufficient  extent.  AS  a  map  is  necessarily  of 
limited  extent,  the  contours  may  not  close  within  such  a  limit. 

About  a  peak,  or  within  a  depression,  contours  will  appear 
as  closed  curves. 

Contours  cross  each  other  only  when  they  represent  the 
relief  of  an  over-hanging  cliff,  and  then  they  show  intersections. 

Contours  run  up  a  valley  on  one  side,  cross  a  stream  at 
right  angles  and  return  down  the  opposite  side. 

Contours  around  hills  cross  ridges  at  right  angles. 

On  uniform  slopes  contours  also  present  a  uniform  appearance 
as  to  direction  and  spacing.   On  steep  slopes  the  contours  are 
close  together  and  on  gentle  slopes  they  are  wide  apart.   On  a 
plane  or  level  tract,  contours  practically  disappear,  or  at  best 
are  depicted,  where  possible,  by  parallel  lines  very  widely  spaced. 

(181)  Relation  of  Profile  to  Contours. 

If  a  line  -  straight,  broken,  or  curved  -  be  protracted 
upoti.  a  contour  map,  it  may  be  represented  in  relief  as  a  profile. 
The  elevations  are  in  this  case  taken  directly  from  the  contour 
lines  cut  by  the  line  of  profile  at  the  points  of  intersection. 
Thus  profiles  may  be  conveniently  made  in  any  direction  upon  the 
contour  map;  liKewise  lines  may  be  protracted  upon  a  contour  map 
to  show  the  course  (direction  and  distance)  of  such  lines  at  any 


Elem.  of  Surv.  IB         Assignment  23  Page  9 

assumed  grade,  the  grade  being  expressed  in  terms  of  elevation; 
this  last  may  be  reduced  to  per  cent  grade,  where  desired. 

References  : 

Tracy         pp.  337-339 

Raymond       pp.  245-247 

Johnson       pp.  260 
Breed  &  Hosmer         Vol.  I. 


I 


i 


t 


o 

-»^I 

^ 

Ct 


•x 


Elem.  of  Surv.  IB 


Assignment  23 


Page  10 


PROBLEMS 

1.  Complete  the  following  set  of  profile  notes,  draw  the 
profile  (sketching  accurately)  and  show  grade  line  of  2-1/2$  grade. 


Sta.      . 

B.S. 

H.I. 

F.    S. 

Elev. 

|  B  Mj_ 

5.13 

100.  00 

Note  :     In  this  set  of 

0 

; 

6.1 

levels  B.M.  ±,    100.00  ft.       \ 

1 

7.1 

above  datum  has  been 

2 

8.8 

previously  determined; 

T   3   P1 

2.16 

9.80 

I 

B.M.  2  was  found  by  differ-; 

4 

5.9 

ential    leveling;   the    sta- 

5 

7.9 

tions  are  taken  in  inter- 

6     , 

10.2 

vals  of  50  feet. 

T  7   P2 

1.26 

14.02 

8 

4.2 

i 

9 

5.9 

10 

6.9 

T   11  P, 
a 

3.04 

11.75 

12 

4.7 

13 

6.4 

14 

5.3 

B    15  M2 

7.23 

1 

2.  Scale  off  the  ground  surface  elevations  above  grade  from 
chart,  Fig.  64  at  2  +  90,  3  *  30,  3  +  80,  4  -f  35,  4  +  55,  5  +  40. 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 

Correspondence  Course 
Course   IB  Elements   of   Surveying  Stafford 

Assignment  2t 

CBOSS-STCTIQw  LEVELING,    VOLULiES,   EXCAVATIONS 

Foreword ; 

The  aira  of  this  assignment  is  to  give  a  general  treatment 
of  the  use  cf  level  readings  over  an  area  for  obtaining  depths  of 
cut  or  height  of  fill,  these  in  turn  to  be  used  to  measure  quantities 
of  earth  to  be  moved  in  either  cese.   A  review  of  the  methods  of 
computing  volume  vill  also  be  made  v.ith  special  application  to 
such  work  as  is  likely  to  confront  the  engineer. 
Cross  Section 

A  cross-section,  as  used  in  the  sense  here  considered,  is 
found  by  determining  the  area  of  a  transverse  section  cf  road, 
railroad,  canal,  etc.,  at  right  angles  to  tne  line  of  such  road, 
etc   This  arta  is  bounded  by  the  oed  of  the  road,  the  angle  aud 

extent  of  the  sloping  sides,  and  the  profile  of  ssction  at  the 

i 
ground  surface, 

/-  !  ..  f 

In  Fig.  68a  is 
shown  the  cross- 
section  of  a  road- 
way. B  B  ;  is  the 


A' 


^MM/I^_ 


b- 


width  of  road  at 


C  B1 

Fig.    68a 

the    base;   A  i3   and   A*  B'    are  the  sloping   sides   of  an  excavation 
(called   a   cut);   C  C1    is   the   height    cf  the.   ground   above  the  center- 


Elem.  of  Surv.  IE 


Assignment  24 


Page   2 


line   of  the   roa~   when  finished;   AD  is   the   elevation  of   the  ground 
above  the  road-oed  There   it  cuts  the  surface   on  the    left;  and  A1   D1 
is  the  corresponding  measurement   on  the   right.      The    bounding    lines 
of  the  section  are  then  AC'A'B'BA.      Had  the   section  been  an  embank - 
ment  instead   of  a  cut   (i.e.    had  the   read   been  built  up  on  the   sur- 
face  of  the   ground   instead  of   being  dug  away)   the   appearance  might 
be    similar  to  that   shown  in  Fig.    68b.      here  the  road-bed  is  at  top 


D1 


3-  J). 


/ 


i     /    '  i/ 

*  /,  ,  /  /  /» 

\/  '  :  i  '        •    .'      . 


C' 
Fig.    68b 


of   embankment.      In 
Fig-    S8a  it    is  at 
bottom  of  excavation. 
The  areas,    shown  by 
the    shaded  portion, 


in  either   case   are   similarly    oounaed,    ac'A1    being  the   profile   of 
the    section  at  the   grouad   surface. 

For  the   purpose   of  computation,    it   is  necessary  to  know  the 
following:  Width   of   road-Deri  3B',    elevation  of  CC'(depth  below 
center   or  height  above  center),    vertical   heights  AD  and  A'D1,  and 
distances  out  from  center  CD  and  C  D1-      'ihc  area  can  then  oe  found 
by  computing  the  area  of  each  triangle  composing  the  figure  ana 
taking  the    sum,    thus: 

Area   of  Triangle   AdC        =  1/2  BC   x  AD 
"        "  "  A'3'C   =  1/2  B'C   x  A'D1 

11  "  ACC1     =   1/2  CC'    x  CD 

"        "  "  A'C'C   =   1/2  CC'    x  CD' 


Elem.    of  Surv.    IB 


Assignment   24 


Page  3 


The  sum  of  these  partial  areas  is: 

BC  x  AD   B'C  x  A'D'   CC  ' 


CD   CC  '  x  CD' 


22  22 

Observe  that  BC  =  B'C.    each  being  half  the  width  of  road-bed, 
and  CC  '   =  CC'.      Therefore,   the   above  summation  may   be  written  in 
simpler  form: 

(AD  +  A'D1)   BC  +  (CD  +  CD')   CC  ' 
2 

Note:-  The  distances  CD  end  CD1  are  really  measured  at  the  surface 
of  the  ground  in  any  case,  the  points  C,  D,  and  D*  being  beneath 
the  ground  and  inaccessible  for  this  purpose. 

We  have  given 
this  geometric  so- 
lution of  the  prob- 
lem at  the  beginning, 
in  order  that  you  may 


B 


D1 


C       B1 
Fig.  68c 

fully  understand  its  nature  and  the  data  required  in  its  determina- 
tion.  The  v;ork  of  the  level  party  in  cross-sectioning  is  given  as 
follows : 

The  level  is  set  up  at  some  suitable  place  where  readings 
may  be  taken  upon  a  rod  held  at  C',  at  A,  and  at  A1  for  any  section. 
Preferably,  similar  points  on  two  or  more  other  sections  may  also 
De  taken.   This  setting  must  be  convenient  to  some  bench  mark  con- 
necting with  the  general  profile  levels  previously  determined 
along  the  line  of  road.   The  H.I.  is  obtained  by  adding  the  B-S. 
reading  on  B.M.  to  the  elevation  of  B.M.   The  difference  between 


Elenu    of  Surv,    IB  Assignment   24  page  4 

the  elevation  of  the   road-ted   and  the  E-I-    is  the   grade-rod  (the 
rod-reading  for  grade).      The  rod  is  nov»  held  upon  C,   and   this   read- 
ing subtracted  from  grade-rod  gives  the  cut  or  fill  at  the  center. 

Next,   determine  the   elevation  above  grade   of  A  and  A1    (AD 
and  A'D'    in  the   figure).     To  do  this   the  rod   must  be  held  at  a 
point   in  a   line  at  right-angles  to  the    line   of  road  from  C;  the 
distance   out   is  one-half  the  width  of  road-bed  plus  the  he ight 
multiplied  by  the   slope.      Inasmuch  as  the  distance   is  dependent 
upon  the   height  the  correct  position  can  only  be  determined  by 
trial.      Hence,  -ve  -estimate  the   point  where  the   sloping   side  of 
the   road  would   cut  the   ground   surface.      A  rod-reading  taken  here, 
subtracted  from  grade-rod,  infill  give  the  elevation  above   road 
grade.      Compute  the  value   cf  CD  from  the   f ornulc. : 
CD  =  1/2  w  •+•  hs,  where  w  =  width  of  roadway,   h  *  height,   and   s  = 
slope.      Should  this  value  agree  with  the  measured  distance,   the 
rod  has  been  held  at  the   right  place.      Otherwise  the   rod  must  be 
moved   toward  or  av.ay  from  C  until  the  desired  agreement  between 
computed  and  measured  distance   is  found.     A  stake  driven  at  the 
correct  point  as  obtained  above   is  called   a  slope-stake.      On  this 
stake   is  marked  the  amount   of  cut  or  fill  (AD,   A'D')   at  that  point. 
Since  this  can   only   be   done   by  trial,   much  patience  and   careful 

% 

judgment  is  the  price  of  success.   By  much  practice,  one  may  oecorae 
adept  at  setting  slope  stakes,  but  it  is  well  to  understand  fully 
the  theory  and  purpose  in  this  v;ork. 
5)  Slope 

This  is  usually  expressed  in  a  ratio  of  the  distance  horizontal 


Elem.  of  Surv.  IB 


As  sic  rune  nt  24 


Page  5 


to  the  distance  vertical;  as  1  to  1  (one  foot  out  to  cne  foot  up 
or  down);  1-jr  to  1  (a  common  slope  for  compacted  earth);  and  2  to  1 
(loose  earth).   A  slope  of  1  to  1  or  steeper,  even  to  vertical  sides 
is  a  slope  for  rock  sides,  loose  to  solid. 
(184)  Sections 

Sections  are  of  four  different  kinds,  according  to  the  nature 
of  the  profile.   These  are:  (1)  level  section  where  the  section 
profile  is  horizontal;  (2)  three  level  section  where  the  profile 
has  two  different  slopes  from  tne  center  stake;  (3)  five  level 
section  in  which  case  the  rod  must  oe  read  at  five  points  along 
the  section  profile;  (4)  irregular  section  where  the  nature  of  the 
profile  requires  (for  accuracy)  several  rod-readings.   These  are 
illustrated  in  Fig-  69.   Of  these  the  level  section  is  the  simplest. 

The  method  of  comput- 
ing the  area  of  the 
three  level  section 
has  already  been  ex- 
plained.  To  compute 
the  area  of  five  level 
section  in  general 

(referring  to  the 

c 
Fig.  69,  p)  divide 

the   section  into  tri- 
angles,  ABB   and  FA'B  '  , 
and  trapezoids,  EC'CB 
and  C'FB 'C,   the  data 


Elem.  of  Surv.  IB 


Assignment  24 


Page  6 


for  which  are  readily  determined.      For   irregular    sections,    other 
methods  are  usually  employed,  the  common  way    Dein^  to  plot  the 
section  to  a  scale    of  convenient    size  and  measure  the  area  with  a 
planimeter.      The  three   level  and  five    level  sections  nay  also  be 
measured   by  planimeter  applied  to  a  plotted  figure,   but  a   level 
section  is  always  most  easily  computed   by  dividing  into  the  two 
simple  trapezoids,  AC'CB  and  C'A'3'C,   as  shovn  in  Fig.    69   (a). 
The   illustrations  represent  cuts  and  by  inverting  the   figures  they 
will  represent  embankments  as  well. 
(185)  A  side-hill  section  is  one  where  the  slope   of  the  ground 

surface    intersects  the    road-bed.      Such  a  section  requires  both  cut 
and   fill  at  that  point   of  the   road.      The  shaded  portions  in  Fig.    70 

&how  the  cut  (to  left)  and 
the  fill  (to  right).  This 
is  generally  considered  an 
economical  mode  of  construc- 
tion, as  the  material  removed 


A1 


from  the   part  ABC  may    De  used   in  filling  the  part  CB'A1;  hence   roads, 
railways,   and  ditches  are  conveniently  carried  along  hill-sides. 
Much  haulage    is   saved   in  such  construction.      Cross-sections  are 
taken  at   intervals   of    100  feet,    or  50  feet,    or   p.ny   other   conven- 
ient interval  depending  upon  the   character  of  the  ground  surface, 
nature   of  material  to  be  moved,   and    other   varying   considerations. 
Suppose   that  the    interval  between  any  two  adjacent   sections   is   100 
feet,    then  the   material   embraced    by   the   two   sections    (in  this  case 
called  end-sections),   the  ground   surface,    the   road-bed,  and  the 


(186) 


Elex.  of  Surv   Ij         i-.ssi^naent  2^  Page  7 

sloping  sides  forms  a  prism.   Tht  oases  of  the  prism  are  the  end- 
sections,  the  mean  of  which  may  be  regarded  as  the  mid-section  (or 
right  section)  of  the  prise.   The  altitude  of  the  prism  would  be 
100  feet  in  this  case. 

By  applying  the  geometric  formula  for  the  volume  of  the 

A  •*•  A1 
prism,  V  =  L  the  amount  of  the  crut  or  fill  may  be  computed. 


Area  of  end  sections,  A  =  225  sq.  ft.,  A1  =  235  sq.  ft., 

100  x  225  -i-  235 
L  =  100  ft.  ,  then  V 23000  cu.  ft.  ,  and  dividing 

by  27  (no.  cu.  ft.  in  1  cu.  yd.),  we  hc-ve  852  cu.  yards,  -which  is 
the  amount  of  earth  to  be  moved.   Specimen  notes  for  cross-section 
work  are  shown  on  Sample  Notes,  plate  23,  for  a  three  level  section. 
You  -will  note  that  the  stations  (first  column;  start  at  the  bottom 
of  the  page  and  run  upward.  A  .full  station  is  100  ft.,  so  that 
37  f  00  indicates  a  full  station;  next,  is  33  +  00,  then  38  +  60, 
39  +  00,  etc.   The  second  column  gives  elevation  at  C,  the  third 
gives  the  grade  elevation  ac  C-   On  the  opposite  side  of  the  page 
the  difference  of  these  two  elevations  gives  the  depth  of  fill  at 
Ci  at  left  the  upper  number  gives  x,he  height  of  A  above  grade,  the 
lower  number  the  distance  out  from  C;  the  letter  f  indicates  fill. 
At  the  right,  we  have  the  saiue  notation  repeated  for  A1.  Also  an 
additional  reading  is  shown  at  the  left  6.0  ft.  out  from  C  with 
difference  between  reading  at  this  point  and  C  of  3.7  ft.,  an 
irregularity  that  sometimes  occurs. 


Elem.    of  Surv.    IB  Assignment   24    fi>  J  Page    8 

riT* 

Vve  will  now   plot   this   section^   and   proceed  to  the   computation 

of  the  area  for  D        3      E  8.0         C       8.0  B1  D1 

^x3T~^ 

the  purpose   of 
further  illustra- 
tion. 


Trapezoid  LCC'F:  6  x  -5>?   5'Q  -  20.1  sq.  ft. 


14.0 


Triangle 


Triangle  AEF  : 


Triangle 


2  * 


3.7  x  5.3 


8.0  x  4.0 


O 
-•  C* 


-  9.8 


=  16.0   " 


Triangle  CC'A1:  3'° 


•-Z2-     =  21.0  " 
Total  area  of  section      =  69-1  sq.  ft. 

For  section  at  station  38  •*•  00  the  computation  is  as 

# 

follows  (aboreviated  form)  : 

8  x   (1.2  +  3.0)   4  2.3  x   (9.8  +  12.5) 

— — — — — =  42.5   sq.    ft. 

To  compute  the   volume  of  the   embankment  between  end-sections 
at   station  37   and   station  38,    we  first    find  the   geometric   mean  of 
sections.      This   is : 


Mean  section  =  /69. 1  x  42. 5  =  54.2  sq.  ft.   Then  the  volume 


L87) 


on  100  feet  of  line  is:  Vol  =  1  y/A  x  A '  =  100  x  54.2  =  54200  cu.  ft., 

or  200.4  cu.  yds. 

Excavations 


Cross-sectioning   is  also  employed  in  determining  the   amount 


Elem.    of   Surv.    13 


ii.ssign.nent   24 


Page 


of  material    removed  from  excavations   or  the    anount   of  material 
required  to  fill  depressions  over  a   limited   araa,  as  in  the  case 
of  a  pit   (especially  a  borrow  pit,   a  cellar,   eta.) 

In  this  work  the   surface  area   is  divided   into  squares  or 
iKctangles  (sometimes  into  triangles)    of  convenient  size.      Suppose 
the   case    of  a  borrow  pit,   Fig.    71,    divided   into   squarss   10  ft.    x. 

10  ft.,   a  few  portions 


0 


A 

12 
B12: 

C12< 

D 
12^ 

E12 
F12i 
G12i 
H12( 

T 

5.2   12J7.3  12(. 

.4   125 

.7   12= 

.9   126 

.2  126 

.5 
.3 
.2 
.2 
..2 
i.O 
».l 

.5   12? 

.0   12< 

.2  12i 

.4   121 

>.0  12( 

i.O  12< 

.0  12! 

.3   12! 

.8   121 

>.9   12( 

5.4  12f 

.3   12( 

:.4     12( 

>.0   12( 

.7    12( 

.8   12( 

i.6   121 

i.5   12( 

i.2   12 

>.8   12 

i.4   126 

.7   12 

i.6   12( 

i.5   12f 

.3    12J 

..7   12C 

.0   12f 

.4   12( 

..4   12< 

i.5   12( 

j.7   12J 

.8   12! 

J.9   12C 

.2   12 

i.3   I^SV   12 

5.1    12t 

.1   12< 

.3   126.4^3r26.5                 126.2 

126.0   126.6 


Fig-    71 


being  shown  as  triangles 
for   purposes   of  illus- 
tration.     Xhe  dividing 
lines   are   numbered  to 
right  in  the  figure, 
0,    1,    2,    3,   etc,, 
and  downward,  K,  B, 
C,    D,    etc. ,    so  that 
references  nay  be 
readily  made   to  the 
points   of  subdivision 
of  the    area   (ground 
surface; ;   as  the 
upper   left  hand  cor- 
ner   is   AO,   B4,    D2, 
G6,   F3,   and   so  on. 


The   divisions  are    staked   off   on  the   grcuiic1   and   the   designation  as 
above  marked  upon  a    stake   driven   at  each   point  as   also    its  elevation 
above    some   convenient  B-M-    to  which   all   roc-readings  are  referred. 


Elera.    of  t>urv.    IB  Assignment   24  Page   10 

The  rod-readings  are  taken  at  each  point  and  recorced   in  the   notes 
of  the  survey,   and  may  also   oe   shown  upon  a  plot  of  the   area  and 
the  depth  of  cut   (or   fill)  marked  upon  the  stake   at  that  point. 

is  always  held  upon  the   ground,   not  on  the    stake.     A  level 


instrument,    or  a  transit  with  a   level  on  the  telescope,    is  set  up 
at  a  convenient  place  where   observations  may  be  made  upon  a  rod 
held  upon  the  B-M.    and  upon  the  cross-section  points  and  rod-readings 
taken  as  follows:     Back-sight   onB.tt.  ,   fore-sights  on  AO,   Al,  A2, 
and   so  on.      The  elevation  of  the  finished  bottom  of  the  pit  (or 
embankment)   above   datum  having  been  established,    and  the   H.I.    of 
the   instrument  determined   by  adding  the  8-S.    to  the  3.M.  >   the  rod- 
reading,    or  H.I.    for   grade  is  computed.      Then  the  F-S.    readings 
taken  at  the   several  points  subtracted  from  the  a.  I.   for  grade 
will  give  the  depth  of  cut,    or  height   of  fill  at  each  point.     We 
new  have  the   elevation  of  these  points  above  the    uottom  of  the  pit, 
or  the  height   of  the   top  of  the  finished  eabanKn-ent  measured  from 
the  ground   surface.      You  will  observe  that  we  now  have  the  dimen- 
sions of  a  number  of  prisms,    each  right  section  of  which  is  the 
same  in  the   length  and   breadth.      The  dividing  up  of  the  ground 
surface   in   uniform  figures  both  simplifies  the  measurement,   and 
as  you  will   presently   see,    lessens  the   computations  as  well.      The 
length  of   each  edge   of  any  particular   prism  is   given  by  the   ele- 
vation of   its  corners,    obtained  as   explained  above.     But  we  require 
the  mean  length  of  each  prism  which  multiplied  by  the  area  of  its 
right-section  will   give  the   volume   of  the   prism.      To  obtain  the 


Elera.  of  Surv.  IB          Assignment  24  page  11 

mean  length  of  the  prism  add  together  the  elevation  of  the  several 
points  of  the  ground  surface  and  divide  the  sum  by  the  number  of 
points,  i.e.  the  nunber  of  edges  -  usually  four. 

Referring  to  Fig.  71,  the  prism  AC,  Al,  Bl,  BO,  would  be 
found  by  taking  1/4  the  sum  of  elevations  at  AO,  Ai,  BO,  Bl,  and 
multiplying  by  100  (=  10'  x  10',  the  dimensions  of  the  right-sec- 
tion); the  prism  Al,  A2,  B.2,  Bl  likewise  has  a  volume  equal  to 

100  x(Al  +  A2  -*•  Bl  +B2/ 

i 1   and   so  on.      You  will   see  that,  tne   right 

section  is  uniform  over   the  whole  area   cowered  by   squares.      The 
right-section  H2,   H4,   J2  is  reacily  computed,    being  a  triangle 

1C  x  20 

,  hence  100  sq.  ft.;  while  the  triangles  G4,  G5,  K4,  and 

G5,  G6,  H5  have  each  a  right  section  of  1/2  (10  x  10)  =  50  sq.  ft. 

A  further  study  of  Fig.  71  will  make  plain  that  if  we  take 
the  elevations  of  all  cross-section  points,  we  will  have  used  AC 
once,  Al  tv.ice,  El  four  times;  or,  from  another  point  of  view,  at 
every  exterior  corner  the  elevation  is  used  once;  every  outer 
point  other  than  these  is  used  twice;  while  every  interior  point 
is  taken  as  many  tirr.es  as  there  are  squares  having  a  common  corner. 

The  depth  of  cut  or  fill  for  each  point  may  be  listed  in 
columns  which  are  headed  1,  2,  3,  4,  to  shorr  the  number  of  times 
each  quantity  enters  into  the  computations.  We  shall  list  them 
by  the  coordinate  numeration,  but  in  actual  work  the  depth  of  cut 
(or  fill)  should  take  the  place  of  this  designation.   This  is 
given  here,  not  as  £  numerical  example,  but  as  a  general  illus- 
tration of  the  method. 


Elem.  of  Surv.  IB 


Assignment  24 


Page  12 


The  total  in  column  1  is  taken  1/4  times;  in  column  2,  2/4 
times;  in  column  3,  3/4  times;  in  column  4,  4/4  times.   Jhe  grand 
total  of  these  is  multiplied  by  tht  area  of  cross-section  of  one 
prism  (iO1  x  1C'  =  100  sq.  ft.);  this,  divided  ay  27,  gives  the 
number  of  cubic  yards.   To  this  must  be  added  the  irregular  portions, 
consisting  of  the  three  triangular  sections  partially  computed. 

4       Irregular  Sections  ' 


AO 

Al 

G4       Bl 

A6 

A2 

H2       32 

^    H2,   H4,    J2 

G6 

A3 

HI       B3 

E4 

A4 

B4 

10  *   2°  -   100    -q      ft 

J2 

A5 

B5 

2 

Jl 

B6 

Cl 

16.3 

HO 

C6 

C2 

16.5 

D6 

C3 

16.6 

E6 
F6 

C4 
C5 

3)49.4  =  16.5 

G5 

Dl 

113 
GO 

D2 
D3 

16.5  x   100 

27             cu.   yd 

FO 

D4 

• 

EO 

P5 

@ 

DO 

El 

^£)H-i,   G4,   G5  and  G5,   G6  ,   H6 

CO 

E2 

16.3 

BO 

S3 

16.4 

E4 

16.4 

E5 

16.1 

Fl 

16.2 

F2 

16.5 

F3 

6)97.9  =  16.6 

F4 

F5 

16.6  x   100 

Gl 

27 

G2 

G3 

Elera.    of  3urv.    IB  Assigiuaant  2* ..  Page   13 

PROBLEMS 

i  C     4  \  **  /•    *4n  Vo  - 

1.    From  data ..  fci-ven    in  notes,  -platv-84%  compute  the  area   of   sections 

at   stations  40  and   4l  and  also  the  volume   in  cu.    yds.   of  earth  to 
be  moved. 

Station    Surface    Grane     Left      Center    Right 


41  118.0  110.9         C  — -  7.1  C 


22.0  19.3 


110.1          C^g  4.6  C^ 

Width   of  roadway    in  cut   20  feet. 


2.  From  data  given  in  the   illustration,   Fig.   71,  compute  the 
amount   of  material    to  be  exce.vated   to  bring  the  pit  to  a   depth 
having  a  uniform  elevation  at   the   Oottoa  of  the   pit  which  will 
be    110  feet  above  datum.     The  cross-section  checks  are   10'   x.  10'. 
Follow  the   order  given  in  the  columns  marked  1,    2,   3,   4  on  page 
12  of  this  assignment. 


References : 


Tracy  pp.428   -  434 

Raymond  pp.275   -   280 

Johnson  pp.    394   -  399 

Breed  i  Hosruer  pp.    2^0  -   2*4 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 

Correspondence  Course 

Course   IB  Elements  of  Surveying  Stafford 

Assignment   25 

VOLUMES  of  CUTS  and  FILLS  (Continued) 

Foreword 

Extended  consideration  of  cuts  and  fills  and  additional  methods 
of  computing  volumes  will  be  treated  in  this  assignment,  as  -well  as 
the  estiaation  of  quantities  in  grading  from  contours. 
L88)       Over  extended  areas  the  methods  of  computing  volumes  of 
earthwork  to  be  moved  are  modified  to  suit  the  greater  magnitude 
of  the  operation.  This  is  done  especially  where  an  approximate 
value  suffices  in  the  estimate.  But  in  some  instances  the  more 
exact  method  by  the  prismoidal  formula  is  both  expeditious  and 
readily  applicable,  and  gives  more  accurate  results.  The  end-area 
method  ie  sufficient  for  most  estimates  and  gives  results  often 

within  the  desired  limits  of  accuracy.  The  volume  of  a  prisiaoid 

L 
is  v  =  "g  (A.i  +  4AJJJ  •*•  Ag).   If  the  dimensions  for  these  computations 


are  taken  in  feet,  the  volume  will  be   in  cubic   feet,  -which  may  then 
be  reduced  to  cubic  yards   (the  common  unit  for  expressing  volumes 
of  earthwork,/   by  dividing  by  27.      In  the  formula  L  is  the  length 
of  the  prismoid;  A^  and  Ag  are  the  end   sections;  A^  is  the  mid- 
section.      This  mid-section  is  not  the  mean  of  the  end   sections, 
but  is  found   oy  taking  the  mean  values   of  dimensions   of  the  two 
end   sections   or   by   actually   taking  the   necessary   data   at  mid-posi- 
tion for  determining  the   section  area  et  that   part. 


i 


i 


Ks 


S^  T* 

S        * 


f 


k 


i    ,P 


:S. 

:   -^ 


.^s 


IN 


& 


^ 


I 


tt 

u 


v? 

$S 


t 


V 


fes 


\ 


S  &   ^ 


«  \ 
x 


Q 


r 


3- 


5 


?P 
55 


ff>^ 


^^ 


.I»6 


^^ 


4 


^K 


ik 

tSa 


i 


5» 


- 


L 


- 


-4— 


5 


-S 


— 


- 

i* 


•:i 


CCS 

I          ^ 


•x 


a 


,  ,    . 


it 


Elera.    of  Surv.    IB  Assignment  25  Page  2 

'I  he  cross-sections  are  usually  taken  at   intervals  of   100 
feet,   50  feet,    or  25  feet.     Where  the  prismoids  thus  determined 
are  fairly  uniform,    it    is  practicable  to  unite  two  consecutive 
stations,   thus  making  the  cross-sectional  area  of  the  intermediate 
station  the  mid- sect ion  of  the  combined  prismoid  thus  formed;   in 
this  case   the  value  of  L  will  be  200  feet  for  full  stations,   or 
100  or  50  for  50 's  and   25 's. 

By  referring  to  Fig.    72,    it  may  readily  be  understood  that 
the  corresponding,  dimensions  of  the  mid-section  may   be  obtained  by 
taking  the  mean  of  the  end-sections. 

Ci  +  C?                    di    +  dp                 hs  -*•  ho 
Cm  = ; I-,   dm  =  — : _,   hm= — = ,   etc.      The  width,  w, 

C*  C     •  w 

'   of  the  r.oadbed  is  the   same  throughout,   hence  no  change  is  made  for 
this  dimension  »t  the  mid-section. 

In  computing  the  cut  or  fill  over   large   areas  the  work  of 
computing  is  greatly  simplified  by  checking  off  the   area  graded  in 
dimensions  that    lend  themselves  tc  ready  reduction. 

The  general  formula  for  volume  in  excavations  or  fill  is 

V  =  -^-  (-~) 

in  which  A  =  ground  area  of  a  uniform  section, £h  =  the  summation 
of  depths  of  cuts  (or  heights  of  fills).  Dimensions  are  taken  in 
feet,  and  feduced  to  cubic  yards  by  dividing  by  27.  Now  write  the 
formula  in  the  form 


El  era.  of  Gurv.  IB. 


Assignment 


Pago  2b 


Figure  72 


Elem.    of  iSurv.    IB 


.  Assignment   25 


Page  3 


If  the  checking  of  the  surface  be  in  rectangles  30'  x  36 '  and  h 
be  taken  to  the  nearest  tenth  of  a  foot,  it  may  be  seen  by  substi 
tuting  above  values  that 

30  x  36   ,__,  . 
V  =  (2h)  cu.  yd. 


27  x  4 

1080 
103 


cu.  yd. 


Which  means  that  the  volume  is  found  simply  by  summing  the  h's 
and  dropping  the  decimal  point.   The  surface  might  also  be  checked 
18'  x  60',  or  12'  x  90' -  Or,  by  retaining  the  decimal  point,  the 
dimensions  of  the  rectangular  checks  may  be  9'  x  12 ' ,  or  6'  x  18 '. 

By  giving  each  problem  a  little  thought  before  beginning 
the  collecting  of  data  it  is  often  possible  to  simplify  the  work. 
^139)       Still  another  method  of  finding  the  volume  of  earthwork  in 
grading  is  found  in  the  use  of  contours  as  laid  down  upon  a  topo- 
graphic msp  of  the  area.  This  method  is  especially  applicable  to 


Figure  73 


Elem.  of  Surv.  IB         Assignment  25  Page  4 

large  areas,  or  for  estimates  generally.  Take,  for  instance,  the 
case  of  a  hill  that  is  desired  to  be  reduced  to  the  level  of  the 
surrounding  terrain.   In  Fig.  73  is  shown  a  hill  depicted  by  con- 
tour lines  having  an  interval  of  1  foot.   It  is  desired  to  reduce 
this  to  a  level  of  125  foot  elevation.   The  fcrea  of  each  plane  of 

horizontal  section  would  best  be  determined  by  means  of  a  plani- 

fully 
meter.   This  is  an  area  measuring  device  which  will  be  discussed 

in  a  later  assignment;  (Assignment  30).   That  part  above  contour 
127  to  the  crown  of  the  hill  is  regarded  as  a  cone,  the  base  being 
the  area  of  the  section  at  contour  127.   The  volume  of  this  part 

will  be  equal  to  1/3  h  Ai  (-  —  ^\Ai).   To  find  the  volume  of  that 

#  6       '    •*• 

part  embraced   between  contours   127  and   125  it  is  necessary  to 
know  the  areas  A^,  Ag  and  A,.      Here  it  is    better  to  use  the  pris- 
moidal   formula  regarding  area  at   section  of  oontour    126  as  the 
mid-section.      The  volume  of  this   portion  will  be  then  V  =  7(A-i  +  4A^,  +  A,); 
hence  the  total   volume   is  expressed  as  follows: 

^ 

Total  Vol.    =  —  C5A.-,    +  4A2  +  A_). 

It   is   sometimes  desirable  to  grade  a   large   surface,  changing 
its    slopes  and  elevations  for   landscape  purposes.      For  this  work 
the  contours  are  determined  and    sketched  upon  a   map   of  the  area 
with  a    suitable   interval.      ±he  contours  of  the  finished   surface 
are  then  drawn  upon  the  map,   preferable  in  a  color   different  from 
that  of  the  primary   contours.      The  drawing  of  the  two  contour 
systems  over  the  same  area  shows  prismoids  whose   lengths   are  the 
contour  interval  and  whose  end  areas  may   readily  be  measured  by 


Elem.  of  Surv.  IB         Assignment  25  Page  5 

planimeter.  (Assignment  30)   If  it  is  desired  to  apply  the  pris- 
noidal  formula,  two  adjacent  prismoids  may  be  comoined  and  the 
common  section  will  constitute  the  mid-section.   In  Fig.  74  the 
heavy  lines  depict  the  contours  with  a  5  foot  interval  as  drawn 


Figure  74 

upon  a  map   of   an  area   to  be  reduced   to   a  grade   as    shown  by  contours 
represented   by  the    long-dashed   lines.      Tr.e    sections   in  each  pris- 
moid   are    shaded,   the  section-areas  may  be  found   by  planiraeter   or 
othenvise.      The  volumes  will    oe  V   (cut)    =  —  (A-,    -t-  4Am  -r 


V(fill)   = 


4a 


a2) 


m 

Here  the  material   removed    oy  cut   is   conveniently   used   to  make  the 
necessary  fill,    any  excess   of  course   to   oe    removed 


Elem.    of  Surv.    IB  Assignment  25  Page  6 

Other  applications  of  these  methods  may    be  employed  on  roads, 
dams,   embankments,   etc.      The  ingenuity  of  the  engineer  may  suggest 
a  large  variety  of  uses  of  such  methods,   by  which  much  time  and 
money  may  be  saved;   especially  is  this  true  in  computing  earthwork 
in  estimates  where  a  high  degree   of  accuracy  would  prove  expensive. 

References  : 

Raymond,   pp.    281-286 
Breed  £  Hosmer ,   pp.    390-395 
Johnson,   pp.    399-405 
Tracy,   pp.    435 


Elem.    of  Surv.    IB 


Assignment  25 


Page  7 


PhOBLLMS 


Problem  1.     Given  the  following  data  of  cross-sections  of   a  roadway. 
Compute  the  area  of  the  raid-section  and  find  volume   in  cubic   yards 
by  the  prismoidal   forraula.    L  r  100  ft.,  w  -  20  ft.,    slope  =  1/1, 

Sta.      Surface     Grade Left     Center     Right 

c       f 


72  33.9         26.5 


71  30.2         25.0 


8.5 
18.5 

6.3 
16.3 


7.4 


5.2 


4.8 
14.8 

2.6 
12.6 


Problem  2.      A  lot   150'  x   144'    is   below  grade  and   is  to  be  filled  to 
bring  it  to  a   level  of  125  ft.    above  datum.      To  compute  the  volume 
of  material  required  the  ground  surface  was  checked  in  rectangles 
having  dimensions  30'  x  36'    and   rod-readings  taken  at  intersections, 
as   shown  on  sketch.      Find  the  volume   in  cu.   yards. 

llfl.fi        18.9       19.2         19.8         19.0        18. 7 


118, 
117, 
116 
115 

3         18, 

1         18 

1         18, 

0        18, 

5        18 

3 

1 
0 
3 

0        17, 

5        17 

6         17. 

7          18 

O         18. 

4        16. 

9         16 

4        16. 

2         16 

0       16J 

2        15. 

8         16 

0         16 

;2      15 

8        15 

OF  CALIFORhLh.  EXTENSION  DIVISION 
Correspondence  Course 

Course  IB  Elements  of  Surveying  Stafford 

Assignment  26 

CTIY  SURVEYING 
Foreword 


A  general  consideration  of  ^ity  Surveying  and  the  laying 
out  of  streets  and  city  blocks  with  their  grades  will  be  considered 
in  this  Assignment. 
(190)  Instruments 

In  general  the  instruments  used  in  city  surveying  should 
be  of  a  higher  degree  of  refinement  than  those  used  in  country, 
farm,  and  highway  work.  This  is  partly  for  the  reason  that  the 
property  -  l?nds,  buildings,  end  other  municipal  improvements  - 
is  of  greater  value,  and  partly  because  of  the  permanent  nature 
of  all  structures  of  a  public  character.   On  the  farm,  the  value 
of  the  land  covered  by  survey  is  usually  a  few  hundred  dollars 
per  acre,  while  city  lands  re£.ch  a  value  in  many  cases  of  hundreds 
or  even  thousands  of  dollars  per  foot  of  frontage  upon  the  street. 
Furthermore,  many  buildings  are  ouilt  upon  the  street  line  and 
upon  the  property  lines  that  divide  one  landowner's  holdings  from 
those  of  his  neighbor,  desicles,  the  grades  of  streets,  surface 
and  underground  drainage  systems,  sewers,  waterpipes,  curbs,  side- 
walks, andthe  like,  must  be  determined  with  great  accuracy.   The 
quantities  obtained  in  the  survey  enter  into  computation  in  esti- 
mates of  costs  of  materials  and  construction  that  run  into  large 
and  often  enormous  sums. 


Elein.  of  Surv.  IB        Assignment  26  Page  2 

i:ence,  in  country  surveys,  the  compass,  and  chain  usually 
suffice,  and  at  best  a  good  transit  and  a  tape.   In  oity  work, 
however,  a  more  refined  transit,  reading  to  30,  20,  or  10  seconds, 
and  a  tape  carefully  compared  with  a  standard  is  necessary. 
Measurements  to  a  high  degree  of  accuracy  should  be  taken  with. 
both  instruments.  With  the  transit  angular  values  to  the  nearest 
5  or  10  seconds  should  be  obtained,  'with  the. tape  measurements 
to  the  nearest  thousandth  of  a  foot  are  necessary. 

On  much  city  work  leveling  should  be  made  to  the  nearest 
hundredth  of  a  foot,  and  on  bench  marks  to  the  nearest  thousandth. 
For  the  latter  a  precise  level  and  a  straight,  carefully  graduated 
rod,  having  a  vernier  reading  to  thousandths,  should  be  used.   You 
should  consult  the  descriptive  catalogues  of  instrument  makers 
showing  the  high-grade  instruments  made  Dy  them.  All  makers  turn 
out  precise  instruments  possessing  features  of  special  excellence, 
and  intelligent  selection  cannot  be  made  without  a  knowledge  of 
several  different  makes. 

(191)        Most  city  surveying  is  conducted  in  cities  already  built  up, 
where  a  fev;  hundred  or  a  few  thousand  people  have  come  to  live  to- 
gether before  the  necessity  for  accurate  surveys  h£.s  been  realized. 
in  some  cases,  however,  a  city  may  be  laid  out  at  the  start,  and 
much  of  the  important  basis  lines,  angles,  and  grades  established 
before  any  population  has  come  upon  the  land.   In  the  former  con^ 
dition  there  are  many  things  that  may  interfere  with  a  desired  or 
proper  basic  survey;  in  the  latter,  these  interferences  oeing 
Banting,  the  character  of  the  beginnings  in  a  city  survey  often 


Elem.  of  Surv.  IB         Assignment  26  Page  3 

devolves  upon  the  engineer  whose  duty  it  is  to  devise  and  perfect 
a  suitable  plan. 
(192)       In  planning  a  city  the  size  of  the  blocks  is  usually  the 

first  consideration,  as  many  things  connected  with  convenience  in 
the  residence  districts,  such  as  lawns,  garden,  out-buildings, 
etc.,  appeal  to  the  early  settlers  in  a  new  town,  while  many  con- 
siderations affect  the  business  district.  But  by  far  the  most 
important  matters  for  careful  consideration  are  the  widths  and 
grades  of  streets,  surface  drainage,  and  sewers  and  sewage  dis- 
posal. The  directions  of  streets  and  their  relation  to  the  car- 
dinal points  of  the  compass  also  deserve  attention. 

Streets  in  the  business  district  should  be  generally  80 
to  120  feet  in  width  with  small  blocks  of  about  225  feet  square 
divided  by  an  alley  parallel  to  the  main  streets  of  15  feet  width. 
In  the  residence  district  olocks  may  be  of  300  to  400  feet  in 
length,  the  alley  may  be  dispensed  with,  and  streets  narrowed  to 
60  feet.  The  subdivision  into  lots  may  be  made  25  feet  wide  in 
the  business  district  and  40  to  50  feet  wide  in  the  residence 
section. 

5)       The  position  of  a  tov/n  site  is  usually  determined  by  one 
or  more  of  several  considerations.   These  are:  nearness  to  a  body 
of  water  or  navigaole  stream  or  to  railroad  station,  or,  in  some 
cases,  to  a  political  division.   Or  the  site  may  conform  to  a 
subdivision  of  a  U.  S.  L&nd  Survey.  To  such  original,  determined 
location  there  may,  of  course,  be  added  from  time  to  time  other 
territory  that  may  render  the  original  plan  more  or  less  irregular 


Elem.  of  Surv.  IB 


Assignment  26 


Page  4 


and  introduce  problems  that  call  for  the  best  skill  and  judgment 
of  the  surveyor.   Such  problems  relate  to  the  streets,  grades, 
surface  and  under  evound  drainage,  sewers  and  sewage  disposal,  as 
was  the  case  -with  the  original  site. 

The  matter  of  defining  these  things  is  largely  in  the  hands 
of  the  engineer  employed  upon  the  surveys,  'out  the  final  disposal 
of  these  matters  is  through  act  of  the  governing  body  of  the  town 
or  city  and  is  usually  in  the  form  of  ai  ordinance  or  ordinances. 
Lines,  grades,  and  the  like  are  said  to  be  established  when  the 
board  of  trustees,  councilmen,  or  aldermen  affirm  certain  defined 
lines  and  grades  by  enactment.  An  "established1'  line  or  grade 
controls  all  others  within  the  city. 

When  the  line  of  a  street  and  its  width  and  grades  have 
been  established,  it  devolves  upon  the  city  engineer  to  set 
proper  monuments  and  bench  marks  so  that  other  engi- 

neers, surveyors,  and  land  owners  may  construct  streets,  curbs, 
fences  (on  property  lines),  buildings,  bridges,  and  other  perma- 
nent features  in  conformity  therewith. 

To  accomplish  this,  center- lines  and  intersections  must  be 
carefully  determined  by  survey,  stone- bound e  that  are  properly 
witnessed  by  tie  lines  must  be  set,  and  their  position  must  be 
indicated  correctly  upon  suitable  maps.   It  is  also  expedient  to 
chart  profiles  of  principal  streets,  so  that  the  ground  surface 
and  the  establishad  grade  may  be  fully  shown  so  that  future 


El em.    of  fiurv.    IB.     Assignment  26,   page  4a 


tO 
eo 


CC 


00 


f 

1 


Grade 


CM 
tO 


10 


U _85_°  0'   W ". 

>•  Grade  -gfo         •{-, 


o 

rH 

105   in 

CM 

10 

rH               in 
rH              CM 

CM 
rH 

in 

CM 

rH              CM 

T(<          in 

rH              CM 

in 

rH 

in 

CM 

o 


10' 


Figure   75. 


co 


CM 


Grade  f$    <— 


0 

rH 

105' 
in 

CM 

rH 

rH 

in 

CM 

CM 

rH 

in 

CM 

tO 

rH 

CM 

r-t 

in 

CM 

LO1 

in 

CM 

CD 
rH 

CM 

rH 

in 

CM 

00 
rH 

in 
105'   "^ 

6 

t 


jxJoft.... 

A— 

( 

...J...5QA.. 


.0 

«a  Grade 


o> 

-c 

05 

wj   o 


a 


o 

in" 


10 


105' 


Ci 


CO 


<£> 


y          j3  85°  0'   E 

™A~~" 


in 


105' 


CM 


(O 


10' 

105' 

105'          0 

CO 

rH 

- 

CM 
rH 

» 

to 

rH 

m 

<o 

rH 

r-l 

« 

in 

rH 

eo 

ID 

rH 

CM 

^ 

H 

i   nf           105' 

15k 

CO 

105'          •* 

1   8' 

Elem.  of  Surv.  IB         Assignment  26  Page  6 

along  the  side  street.  The  center  lines  of  the  side  streets  are 
now  run  at  the  proper  bearing,  and  the  mid-points  of  the  alley 
ways,  the  location  of  the  property  corners,  curb  lines,  and  other 
points  are  staked  out.  Curbs  are  finished  with  rounded  corners 
but  in  the  survey  the  stakes  are  driven  at  the  points  of  inter- 
section at  the  corner. 

When  the  town  is  laid  out  before  being  built  upon,  the  system 
of  streets,  blocks,  alleys,  curb-lines,  etc.,  can  be  surveyed  with 
strict  conformity  with  a  uniform  plan  as  shown.   In  such  case,  the 
lots  also  may  be  staked  out,  a  tack-centered  hub  placed  at  each 
corner,  witness  or  guard  stakes  should  also  be  driven;  on  these 
should  be  placed  the  lot  and  block  numbers  to  serve  for  identifi- 
cation in  the  field. 

While  the  business  portion  of  a  city  should  have  a  more  or 

less  rectangular  plan,  the  residence  districts  may  conveniently 
i 

conform  with  the  topography  of  the  region;  the  streets  may  even 
follow  principal  contours  over  hilly  portions  thereby  conserving 
both  grade  and  direction;  the  individual  lots  in  such  cases  may 
be  quite  irregular  in  shape  and  size;  here  attention  must  be  given 
to  frontage  and  depth  to  afford  a  suitable  ouilding,  site  with 
proper  lawn  and  garden  and  apace  for  necessary  out -buildings. 

Streets  may  intersect  at  all  conceivable  angles  ano  turn 
upon  regular  curves  both  horizontal  and  vertical.   Horizontal 
curves  such  as  are  required  in  railroad  construction  are  commonly 
employed,  but  these  are  generally  of  simple  kin<?,  end  can  readily 
be  laid  out  by  the  usual  methods  in  such  cases. 


Elern.    of  burv.    IB 


Assignment  26 


Page  7 


(196)  The  Simple  Curve 

In  Fig.  76,  m  Fnd  BD  arethe  center  lines  of  two  streets 
intersecting  at  B-   It  is  desired  tc  connect  these  by  a  curve, 

•which  should  be 
tangent  to  both 
lines  of  roadway. 
The  deflection 
angle  EBD,  called 
here  the  inter- 
section angle,  is 
measured.  A  suit- 
able degree  of 
curve  is  then  de- 
termined and  its 
radius  computed. 

To  do  this  it  is  necessary  to  make  certain  assumptions.   These  are 
as  follows: 

1.  The  curve  is  laid  out  by  chords  of  regular  length, 
usually  100  ft.  long. 

2.  The  number  of  such  chords,  dependant  upon  the  ratio  of 
the  intersection  angle  to  the  degree  of  curve,  will  govern  the 
length  of  the  curve,  and  hence  the  curve  may  begin  at  any  point 
assumed  on  either  tangent  AB  or  BD-   In  railroad  surveys,  it  is 
the  practice  to  make  each  station  on  the  line  100  feet  and  in  most 
cases  the  point  of  beginning  of  a  curve  is  not  coincident  with  a 


.  of  Surv.  IB         Assignment  26  Page  8 

full  station^  therefore  fractional  chords  are  common.  But  as  sta- 
tioning is  not  practiced  in  city  surveying,  it  is  the  practice  to 
begin  curves  at  the  point  of  beginning  and  to  close  on  the  point 
of  closing  when  convenient. 
(197)       In  the  figure,  perpendiculars  are  drawn  to  the  points  of 

tangency  of  the  curve  joining  AB  and  BE;  thus  the  angle  C,  called 
the  central  angle,  5.s  constructed.   It  will  be  seen  that  angle  I 
equals  angle  C.   If  we  wish  to  make  a  given  number  of  chords,  n, 
then  we  divide  the  angle  I  (a  C)  by  n  which  gives  us  the  degrees 
of  curve.   Having  chosen  the  degree  of  curve,  with  this  considera- 
tion, it  is  necessary  to  know  the  points  of  tangency,  i.e.  the 
tangent  distance  of  P.O.  and  P.T.  (point  of  curve  and  point  of 
tangent,  respectively).   The  geometric  relations  of  these  points 
are  as  follows: 

—  =  degree  of  curve  (D) 

Radius  of  curve  =  ~  -t  sin  ?  =  —  1/2  D 

2       2   sin 

I          C 
Tangent  Distance  =  R  •  tan  —  (=  R  •  tan  — ) 

Ci  & 

We  may  now  locate  P.C.  and  P.T.;  this  is  done  and  tack  centered 
hubs  are  driven  at  both  points. 

To  lay  off  the  100  foot  chords  from  P.C.  to  P.T.  ,  it  is 
necessary  to  know  the  amount  that  each  chord  deflects  from  the 
tangent  AB.  Draw  the  line  P.C.  to  P.T.;  this  is  known  as  the  long 
chord.  The  angle  formed  by  the  tangent  and  long  chord  intersecting 


Elea.   of  Surv.    IB  Assignment  26  page   9 

at  P.O.    or  P.T.    is  equal  to   1/2   I,   This  angle,   divided  by  the  number 
of  chords   in  the  curve,   gives   the  value   of  each  deflection  from  the 
tengeat.      Hence,   if  n  equals  the  number  of  chords,   and  I  equals  the 
intersection  angle,   then  the    deflection  angle  d   is  found   from  the 

formula  d  -  — .     With  this  angle   laid   off  from  the  tangent,   the 
2n 

first  chord  of  ICO  feet   is  measured  from  P.C. ;  then  with  double 
the  deflection  angle  d  the  second  chord   is  laid  off,   and   so  on 
until  the  curve   is  completed. 

(198)  Let  us  take  a  special  example.      Suppose  that  two  roadways 

intersect  at  an  angle   of  70° ;   it   is  desired  to  lay  out  a  curve   of 

say  five  chords  and  therefore  the  degree   of  curve  selected   is 

T  70 

14°  _  —  =  n  =  — =  5.     The   radius  of  a  14°  curve  will  be: 
D  14 

R  =       50       =       50       =  410.17   ft. 
sin  7°       0.1219 

Tangent  distance  then  is: 

T  =  R  tan   1/2    I  =  410.17  x  0.7002  =  237.2  ft. 
A  deflection  angle   of  7°   is  obtained  from 

d=-L  =  _Z?_  =  7° 
2n       2x5 

To  locate  the  curve  in  the  field  proceed  as  follows: 
Measure  off  the  tangent  distance,  287.2  ft.  from  P.I.  to 
P.C.  and  P.T.   Set  up  transit  at  P.C.  With  vernier  set  at  0°,  upper 
motion  clamped,  sight  upon  P.  I. ,  clamp  lower  motion,  bisect  P.I.  b,y 
use  of  tangent  screw.  Xurn  off  the  deflection  angle,  7°,  and,  with 
100  ft.  tape,  measure  the  first  chord  from  P.O.,  lining  in  head 
chainman  with  the  transit  telescope.  Drive  hub  and  set  tack  center. 


Elem.  of  Surv.  13 


Assignment  26 


Page  10 


Turn  off  2  •—  =  14°,  measure  the    second  chord  from  end  of  the   first 
<cn 

chord,   lining   in  with  transit   telescope  as  before,  and  proceed  thus 
until  the  five  chords  are   staked  out   in  the  field.     As  a  check  set 
up  transit  at  P.T.    and   check  back  on  the   angles;  these  should  be  the 
same  in  reverse   -  7°,    14°,   21°,   etc.      The  curves   of  roadways  may  be 


Figure  77 


compounded,  as  in  case  of  several  tangents  intersecting  at  differ- 
ent angles,  the  deflections  being  either  in  the  same  direction  or 
in  reverse  as  shown  in  Fig.  77,  a  and  b.  The  adjustment  of  tan- 
gent distances  is  a  prior  consideration  to  degree  of  curve  which 

may  be  deduced  from  the  formulas  given  above. 

T         Tan.  Dist. 
Tan.  Dist.  =  R  •  tan    .  .  R  =  j —  ,  and 


since  R  = 


D 
sin  -; 


.'  .  sin  D  =  50  or 
2   R 


Tan 


50  tan 


sin —  —  — — — 

2   Tan.  Dist. 


Elem.   of  surv.    IB  Assignment  26  Page   11 

References; 

Tracy  pp.    188-190 

Raymond  pp.   230-243 

Johnson  pp.    356-370 

Breed  &  Hosmer  pp.    251-275 

Problem  to  accoapany  Assignment  26 

Two  center   lines  of  streets   intersect  at  an  angle  of  60°; 
it  is  required  to  connect  these   streets  by  a  curved  roadway  having 
a  degree   of  curve  giving  six  full  100  foot  chords.     Find  the 
degree  of  curve,   radius  of  curvature,  tangent  distance,  deflection 
angles.      Supposing  the  deflection  to  be  to  the  left,  make  the 
paper   location  of  the  curve   on  a   scale   of  1  inch  ~  100  ft. 


KbiTY  UF  CALIFORNIA  MI-ENSIGN 

Correspondence     Courses 
Surveying   13  Assignment  27  swafford 

Foreword 

A  continuation  of  city  surveying  witia  special  consideration 
of  coordiaats  systems,  irregular  subdivisions,  andsubdivisions  of 
additions  to  townships,  will  oe  the  wor*  of  this  assignment. 
(199)  Street  Grades 

While  street,  grades  depend  largely  upon  the  topography  of 
the  town-site,  it  ic  always  desirable  to  reduce  these  as  nearly 
to  level  as  is  consistent  with  good  drainage.  Where  the  land  is 
especially  irregular  and  hilly,  streets  should  conform  as  nearly 
as  possible  to  the  relief  features  in  order  to  preserve  beauty  of 
landscape.   Yet  tne  v?hole  must  be  treated  ia  such  a  way  as  to 
afford  ccave.iie.it  and  orderly  arrangements  of  olocK.6  and  streets 
go  that  tne  citj  ma;:  possess  proper  order  in  ootn  its  business 
and  its  residential  districts.  A  strict  adherence-  to  rectangular 
forms,  straight  streets,  and  uniform  blocks  may  prove  difficult, 
but  as  a  city  grows  in  size  and  easiness  importance,  these  things 
become  of  greater  and  greater  significance.   Hence  ia  planning 
cities  consideration  .nust  oe  given  to  such  matters,  for  otherwise 
many  difficult  prcalems,  such  as  the  videning  and  straightening 
of  streets,  changinfc  of  grades,  etc.,  will  oe  lively  to  arise  in 
the  future.   Such  changes  e.re  attended  with  great  expense  and  are 
often  the  cause  of  much  troublesome  bickering  and  litigation. 

So  far  as  possible  street  grades  should  conform  to  the 
grades  of  property  along  the  street;  otherwise  either  the  street 


Survey  ing  13 


27 


Page  2 


•work  becomes  too  costly  or  much  filling,  or  leveling  is  required 
to  bring  the  property  into  grade  suitaole  to  the  roadway,   i'hs 
gradient  of  the  street  should  oe  established  with  regard  to  the 
many  matters  aoove  referred  to,  end  improvements  relative  to  the 
construction  and  maintenance  of  curbs,  to  drainage,  and  to  road- 
way should  be  conducted  in  accordance  with  them. 

(20C)        In  the  case  of 'irregular  shaped  DlocKS,  it  is  often  uncer- 
tain whether  the  lot  lines  should  run  perpendicular  to  one  street 
or  another  and  also  whether  for  the  sake  of  uniformity  the  lots 
should  extend  longitudinally  in  one  direction  or  another. 


Figure  78 


In  Fig.  78  it  IE.  of  course  desirable  that  the  frontage  of 
blocks  shall  be  upon  kain  St.  (here  supposed  to  be  a  principal 
business  street),  out  it  is  also  cesiraole  that  the  lot  lines  shall 
be  perpendicular  to  the  line  of  Main  St.   The  oblique  angles  are 


Surveying  13  Assignment  27 

net  oojeccicueole  provided  the  ooliquity  is  not  great,  as  shown 
on  Clark  Ave.  ;  still,  ay  adjusting  the  boundaries,  as  shown  by 
the  dotted  division  lines,  the  lines  may  be  rectified  so  as  to 
preserve  at  the  same  time  the  uniform  width  of  lots  along  Main.  St. 
On  Clark  Ave-  the  oblique  angles  are  not  so  objectionable,  since 
this  is  a  residence  surest.   The  houses  are  set  back  from  the 
street  line  ar.dt.he  sidewlks  are  made  parallel  to  the  street. line. 
Much  ingenuity  and  some  taste  may  be  exercised  in  subdivision 
of  large  irregular  tracts  in  residence  additions,  so  that  roads, 
parking,  and  lawns  may  present  a  picturesque  and  pleasing  appearance. 
Where  such  a  plan  does  not  involve  great  waste  of  land  out  gives 
convenience  of  arrangement  for  building  sites,  streets,  etc.  ,  it 
is  preferaole  to  the  rectangular  and  conventional  regularity  of 
city  lots  that  are  so  common  because  they  economize  space  and  af- 
ford convenient  street  plans. 

(201)      Plans  for  sewers  giving  their  location  both  in  plan  and  pro- 
file should  be  carefully  made  both  to  assist  in  estimates,  con- 
tracts, and  actual  vorli  of  construction  and  also  to  facilitate  the 
making  of  alterations  and  repairs. 

Water  mains,  gas  mains,  and  electric  conduits  should  also  be 
carefully  surveyed  and  mapped  for  like  reasons.  Cities  are  now 
generally  requiring  that  all  such  mains  be  placed  not  in  the  road- 
way but  in  the  parking  v;ithin  the  lines  of  curb  or  through  "ease- 
ments" conceded  b^  property  owners  along  the  rear  lines  of  adjoin- 
ing holdings;  alleys  in  some  instances  take  the  place  of  such 
"easements"  and  are  thus  made  a  public  care. 


Survey ing- IB  Assignment  27  Page  4 

(202)      To  provide  suitable  drainage,  streets  are  built  higher  at 

center  than  at  the  curb  on  either  side.  This  raising  at  center  is 
called  "crowning."  Generally  it  is  sufficient  to  make  the  center 
as  high  as  the  top  of  the  curb-  and  since  the  crowning  is  always 
determined  bj-  the  eleiation  of  the  curb,  it  is  required  that  appro- 
priate  grade  stakes  be  put  in  for  setting  curbs.  This  is  done  by 
setting  a  convenient  bench  irark,  rhich  may  be  brought  up  by  dif- 
ferential leveling  from  some  other  bench  mark  or  datura.  When  the 
relation  of  the  curb  profile  to  this  new  3.  M.  has  been  found, 
grade  stakes  are  set  for  curbs.   Stakes  should  be  driven  firmly  into 
the  ground  along  the  line  of  curb  and  the  actual  elevation  marked  by 
a  line  upon  the  stake  in  order  that  workmen,  who  are  not  engineers, 
may  -vork  to  the  line  designated. 

A  crose  section  of  a  street  from  curb  to  curb  is  shown  in  Fig. 
79.   Here  the  special  case  where  one  curb  is  higher  than  the  other 

is  chosen,  for  the 
case  where  both 
curbs  are  at  the 

same  height  is 
Figure  79 

easily  understood. 

The  crowning  at  C_  is  made  equal  to  the  height  of  curb  at  h  (the 
higher  side).   The  form  cf  the  curve  of  the  finished:  street  is  gen- 
erally parabolic  and  hence  at  points  1,  2,  3,  4  the  depth  below  the 
straight  line  L  L1  is  as  the  square  of  the  distance  from  C  on  either 
side.   The  depth  of  gutters  at  each  side  is  determined  by  the  quantity 


Surveying-IB  Assignment  27  Page  5 

of  surface  drainage  to  be  carried  off,  and  hence  the  height  of  C 
varies  with  this  condition. 

(203)  Widening  and  straightening  of  streets  in  cities  calls  for 
careful  surveys  first  to  determine  the  old  lines  and  then  for  the 
several  plans  to  bring  about  the  most  desirable  revision.  All  such 
changes  are  attended  by  great  expense  and  often  entail  hardships 
upon  property  owners.  Where  practicable,  therefore,  the  most  eco- 
nomical course  should  be  followed. 

(204)  Monuments  of  surveys,  benchmarks,  etc.,  are  made  numerous  in 
cities  owing  to  their  frequent  use  and  they  should  be  placed  at  con- 
venient points  for  reference.  These  can  seldom  be  placed  in  the 
roadways  as  they  are  disturbed  by  traffic,  and  are  likely  to  be 
changed  or  wholly  obliterated  by  street  work  that  is  frequent  even 
in  crowded  thoroughfares.   Hence  all  monumente  and  bench  marks  are 
best  located  on  curbs,  corners  of  buildings,  or  by  specially  con- 
structed structures  not  in  but  on  or  near  the  street.   Often  a  mark 
properly  referenced,  out  into  a  curbstone  may  serve  the  double  pur- 
pose of  a  stone  Dound  and  a  benchmark.   Such  marks  are  inexpensive 
and  can  be  plentifully  established  throughout  a  city,  especially  in 
the  districts  where  they  are  much  needed. 

(205)  The  method  of  laying  out  of  streets  and  city  blocks  as  here- 
tofore described  by  street  lines  properly  raonumented  and  by  a  general 
system  of  rectangular  blocks  is  by  far  the  most  common,  but  a  co- 
ordinate system  is  by  far  the  more  desireable  from  many  considerations. 


Surveying-IB  Assignment  27  Page  6 

The  co-ordinate  system  starts  with  an  initial  point  assumed 
usually  upon  some  established  meridian  and  with  the  two  axes,  Y  in 
conformity  with  this  meridian,  and  X  at  right  angles  to  this  extend- 
ing in  an  east  and  west  direction.  The  corners  of  all  blocks,  lots, 
centers  of  streets,  and  positions  of  public  buildings  are  therefore 
located  with  respect  to  the  intersection  of  these  axes  as  X's  and 
Y's.  The  relocation  of  any  corner,  disturbed  by  any  cause  can  readily 
be  made,  or  monuments  restored  or  established  anew  by  resort  to 
measurements  from  these  axes.  By  such  a  system  the  work  of  the  sur- 
veyor is  at  once  simplified  and  a  higher  degree  of  precision  made 
possible.  Such  systems  are  best  when  made  independent  of  curvature 
and  convergence  of  meridians,  all  north  and  south  lines  being  made 
parallel  to  the  Y  axis,  all  east  and  west  lines  parallel  to  the  X 
axis. 

Triangulation  systems  are  also  in  use  in  some  large  cities. 
These  systems  require  the  establishment  of  a  base  line  determined 
in  position  by  careful  astronomical  observation  and  measured  with 
extreme  accuracy  and  properly  monumented.   Then  as  in  geodetic  sur- 
veying, a  net  of  triangles  beginning  upon  this  base  is  determined, 
•their  corners  are  permanently  marked  throughout  the  territory,  and 
the  primary  survey  proceeds  in  the  usual  manner.  All  angles  are 
measured  either  with  a  direction  theodolite  or  by  the  method  of 
repetition  with  a  precise  transit  capable  of  reading  to  20",  or 
"better,  to  10". 

The  angles  are  adjusted  for  each  triangle  and  any  small  dis- 


Survey ing- IB  Assignment  27  Page  7 

crepancy  in  the  total  interior  measure,  which  should  of  course  be 
180°,  is  distriouted.  The  sides  of  the  triangles  are  then  computed, 
the  lengths  of  all  lines  being  checked  as  the  computation  proceeds. 
(206)      As  before  stated  the  instruments  employed  in  city  surveying 
should  be  of  the  more  precise  kind.  A  tape  should  be  graduated  to 
handredths  throughout  and  compared  with  a  known  standard.   It  is 
best  to  know  the  normal  tension  at  which  the  tape  may  be  used;  and 
as  temperatures  may  vary  greatly  from  time  to  time,  the  temperature 
should  be  taken  with  ee.ch  measurement  requiring  great  accuracy. 
Generally  it  will  be  better  to  take  tape  measurements  along  the 
slopes  and  either  determine  the  angle  of  slope  or  the  difference  in 
elevation  between  the  ends  of  any  segment  of  a  line  where  the  slope 
changes.  The  usual  corrections  are  then  readily  and  accurately  made 
for  obtaining  the  horizontal  distance.   It  is  not  required  in  taking 
the  difference  in  elevation  to  use  an  engineer's  level,  as  a  transit 
with  level  on  telescope  may  be  conveniently  substituted,  and  in  many 
cases  differential  leveling  with  the  hand  level  or  measuring  angle 
of  slope  by  means  of  the  clinometer  will  suffice. 

The  surveyor  on  city  work  should  recognize  that  there  should 
be  different  degrees  of  accuracy  sought  in  the  various  kinds  of 
measurement.   In  all  primary  r:ork  such  as  setting  of  monuments, 
stone-bounds,  benchmarks,  etc.,  measurements  should  be  taken  with 
great  care,  carefully  corrected  for  standard  temperature,  slope  and 
so  forth,  and  each  monument  should  oe  checked  usually  by  a  second 
or  third  set  of  measurements  conducted  bj,  parties  of  a  different 


Surveying-IB  ^.ssigiiment  27  ^age  8 

personnel.   All  monuments  and  stone  bounds  should  be  accurately 
referenced,  so  that  they  may  be  properly  restored  if  disturbed. 
Since  such  points  are  arbitrarily  set  in  the  primary  survey  it  is 
vrell  to  make  these  fall  at  an  even  foot-mark  where  practicable, 
but  the  measurements  taken  in  the  establishing  of  them  should  have 
regard  xo  the  nearest  hundredth  or  possibly  thousandth  of  a  foot. 
Street  lines,  on  which  many  blocks  and  lots  are  likely  to  abut, 
should  be  run  in  conformity  with  a  fixed  meridian  or  its  bearing 
therewith  should  be  c=u-efu?.ly  determined  to  within  a  few  seconds  of 
arc.   This  bearing  may  be  secured  by  use  of  a  precision  instrument, 
a  direction  theodolite  or  a  good  transit,    If  a  transit  is  used, 
the  method  of  reading  angles  should  be  by  repetition,  six  repetitions 
normal  and  six  inverted  and  by  reading  on  varying  parts  of  the  limb 
in  order  to  eliminate  srrors  in  eccentricity  or  graduation. 

Differential  leveling  for  establishing  bench  marks  should  be 
conducted  forward  from  a  permanent  datum,  and  rod  readings  made  to 
the  nearest  thousandth  of  a  foot.   The  level  rod  should  be  accurately 
graduated  and  compared  with  a  standard  tape,  or  carefully  calibrated. 
Readings  should,  therefore,  be  made  upon  targets  and  with  the  use  of 
a  rod  level  or  other  plumbing  device.   The  index  error  of  the  rod 
vernier  should  also  be  determined  and  the  target  setting  for  long  rod 
checked  as  well.   In  short,  r.ll  possibilities  of  instrumental  errors 
should  be  eliminated. 

(207)       The  extreme  Accuracy   c.imed  at  in  work  described  above  is  not 
required  in  measurements  of  secondary  importance,  such  r.s  setting  of 
curb  lines  and  grades,  placing  of  fence  lines,  surveys  for  surface  and 


Surveying-IB  Assignment  27  Page  9 

underground  drainage,  severs,  water  rains,  gas  mains,  electric  con- 
duits, etc.   In  such  surveys  an  accuracy  to  tlve  nearest  tenth  of  a 
foot  and  lines  run  practically  parallel  to  existing  lines  are  suf- 
ficient.  Time  and  labor  on  making  refined  measurements  in  these 
latter  cases  but  add  to  expense  vrithout  securing  a  requisite  degree 
of  precision. 

In  general,  city  surveying  requires  few  data  obtained  in 
the  field,  but  complete  notes  and  clear  accurate  sketches  must  ac- 
company all  field  data  which  also  should  be  immediately  recorded  in 
original  field  books.   These  field  books  also  should  be  labeled 
and  properly  indexed,  in  order  that  the  data  relating  to  any  given 
survey  may  readily  and  accurately  be  found. 

Office  work  consisting  in  the  computations  from  observed  and 
recorded  data,  making  of  naps,  detailed  sketches,  etc.,  should  be 
carried  forward  as  the  work  progresses  and  surveys  are  correlated 
with  other  work  of  record. 

References : 

Johnson,  pp.  356-383 

Tracy,  p.  138 

Raymond,  pp.  230-236 

Breed  &  Hosmer,  pp.  251-286,  Vol.  I. 


Surveying-IB  Assignment  27  Page   10 

Problems 

1.   The  line  of  Main  Street  in  the  term  of  A  bears 
8  17°30'  E  of  true  north;  First  and  Second  Streets  intersect 
Main  Street  at  an  angle  of  87°10',   '.That  is  the  bearing  of 
First  and  Second  Street  lines  with  true  north? 

2o    If  the  lot  lines  on  Li?,  in  Street  are  perpendicular 
to  the  line  of  Main  Street,  -./hat  is  the  bearing  of  these  lines? 

3.   Sketch  Hr.in,  First  and  Second  Streets;  place  arrows 
on  sketch,  showing  both  true  north,  ir.^netic  north  (declination, 
12O15'  Bast)  and  --rite  tha  respective  bearings  on  the  lines  so 
drawn. 


UNIVERSITY  OF  CALIFORNIA  LXTt^oiiON   DIVISION 
Correspondence     Courses 

Surve^ing-lB  Assignment  23  Mr.   Stafford 

RAILROAD     SURVEYING 

Foreword 

In  the  present  course  it  is  the  purpose  to  give  only  a  very 
elementary  treatment  of  the  suoject,  Railroad  Surveying,  as  this 
branch  of  the  work  is  of  a  highly  complex  nature,  presenting  many 
problems  requiring  the  highest  skill  of  the  engineer. 

The  work  in  railroad  surveying  is  divided  into  several  parts, 
the  order  of  progress  depending  upon  the  stages  of  such  work.  The 
three  stages  here  considered  will  embrace  (1)  Reconnaissance  Sur- 
vey, (2)  Preliminary  Survey,  (3)  Location. 
(208)  The  Reconnaissance  Survey 

When  it  has  been  determined  to  connect  two  or  several  locali- 
ties by  a  line  of  railroad  the  first  v;ork  devolving  upon  the  en- 
gineer is  to  reconnoiter  the  territory  to  oe  traversed  and  to  gain 
by  this  means  a  knowledge  of  the  character  of  the  country  -  its 
plains  and  hills,  its  water  courses,  timber,  soils,  rocks,  etc. 
This  is  done  in  order  to  determine  the  most  desirable  and  likewise 
the  most  feasible  or  the  least  expensive  route  to  be  followed  in 
order  to  carry  out  the  purpose  of  the  roac.   It  is  often  necessary 
to  examine  not  one,  but  two  or  more  different  routes  by  which  this 
purpose  may  be  accomplished.  This  part  of  the  uork  constitutes 
the  reconnaissance  survey  which  consists,  in  short,  in  discovering 
the  route  of  the  proposed  railroad. 


Surveying-IB.  Assignment  Ko.  28,  page  2. 

To  do  this  the  chief  engineer  of  the  road,  equipped  ;vith  the 
necessary  instruments  and  accompanied  by  one  or  more  aids,  traverses 
the  territory  choosing  a  route,  or  several  routes.   He  observes  the 
lay  and  character  of  the  land  more  or  less  minutely.  He  should 
travel  slowly  either  on  foot,  where  wagon  roads  are  wanting,  or  by 
light  conveyance  on  such  roads  as  parallel  the  desired  route.   In 
other  words,  he  oust  actually  traverse  the  lines  it  is  intended  to 
follow. 

He  should  be  equipped  T.vith  a  compass,  a  hand  level  (which  may 
also  combine  a  clinometer)  a  field  glass,  and  a  pocket  tape.  A  50 
foot  cloth  tape  is  a  convenient  one  to  handle  and  is  sufficiently- 
accurate.   If  a  wagon  is  used,  a  rodometer  attached  to  one  wheel 
will  be  found  excellent  for  determining  distances  traveled  by  road. 
An  aneroid  barometer  will  liKewise  be  useful  in  determining  eleva- 
tions from  time  to  tiir.e.  The  intermediate  elevations  may  be  deter- 
mined by  observation  with  the  hanc"  level  or  clinometer. 

Over  some  portions  of  the  route  it  ,aay  be  expedient  to  make 
topographic  maps  by  plane-table.  For  regions  i\here  the  Geological 
Surveys  of  the  country  have  been  made  the  \ery  excellent  contour 
maps  published  by  the  Government  Bureau  mav  be  procured.   Such  maps 
should  be  used  not  in  lieu  of  a  personal  examiniation  of  the  ground 
itself,  but  only  as  an  excellent  aid  to  a  better  understanding  of 
the  nature  of  the  territory  traversed. 

The  engineer  should  make  copious  notes,  collect  much  desirable 
data,  and  draw  frequent  sketches  to  assist  his  m;mory.   In  fact  he 
should  trust  little  to  memory  and  never  where  the  data  are  obtainaole 


Surveying-IB.  Assignment  £3,  page  3. 

and  the  record  can  oe  made.   Hie  survey,  when  completed,  should  en- 
able hirc  to  visualize  the  entire  route,  section  by  section,  in  such 
manner  as  to  drav  in  imagination  and  afterwards  in  reality  any  por- 
tion of  the  route  selected;  and  to  indicate  thereon  practicable 
grades,  location  of  bridges,  cuts,  or  tunnels,  and  the  deflections 
of  his  road  from  point  to  point. 

Not  always  does  he  choose  the  most  direct  route  between  two 
given  points.   Such  a  course  often  entails  too  great  an  expense  in 
construction,  as  it  may  require  bridging  a  stream  several  times,  or 
the  making  of  costly  cuts  or  tunnels.  Often  an  engineer  finds  that 
by  keeping  to  the  comparatively  level  lands  along  the  course  of  a 
stream,  even  rhen  the  sinuosity  of  the  stream  is  great,  he  is  able 
to  construct  his  road  at  smaller  cost,  althougn  it  might  be  desir- 
able to  straighten  the  road  subsequently.  Along  the  broad  alluvial 
plains  of  streams  the  cost  of  construction  is  usually  at  the  mini- 
mum, as  it  requires  at  most  only  moderate  embankments  that  shall  keep 
a  road  bed  well  above  any  possible  inundation  in  time  of  freshets. 
Moreover,  the  character  of  the  soil  lends  itself  to  cheapness  in  con- 
struction while  the  gradient  is  altvays  gradual,  approaching  or  fall- 
ing away  from  a  watershed  divide  by  easy  stages.  A  T"ide  detour  is 
often  made  necessary  to  avoid  bridging  or  cuts  thst  would  otherwise 
be  necessary. 

Another  advantageous  location  for  a  road  is  found  in  following 
hill-side  formation  as  the  materials  cut  from  the  upper  portion  are 
at  hand  to  make  the  fill  upon  the  lower  portion.  Ledges  are  often 
found  in  some  localities  that  further  contribute  to  cheapening 


Surveyin°;-13.   Assignment  28,  page  4. 

construction.   Often,  too,  by  means  of  an  occasional  trestle  that 
carries  the  road  o\er  a  small  ravine  one  series  of  skirting  contours 
after  another  .nay  oe  utilized,  and  thus  afford  an  economical  route. 

All  such  matters  as  those  mentioned  above,  \7hich 'the  engineer 
encounters  upon  his  trip  over  the  proposed  route,  are  carefully 
noted,  lines  are  drawn,  elevations  taken,  and  sketches  ua.de  to 
elucidate  the  conditions.  These  are  then  embodied  in  a  report  to 
the  railroad's  board  of  directors.  Before  completing  his  report, 
if  time  and  funds  permit,  the  engineer  should  retrace  his  journey 
noting  alternative  routes  or  plans,  verifying  or  correcting  ob- 
servations, and  choosing  perhaps  the  more  desirable  of  two  routes. 

Out  of  this  mass  of  information  a  plan  is  formulated  and  a 
proposed  route  finally  determined  upon,  v/hich  shall  guide  the  en- 
gineer in  staking  out  upon  the  ground,  by  tangents  and  deflections 
and  by  a  system  of  profiles  more  or  less  conplete,  tlie  defined 
route  of  the  road.  This  survey  constitutes  the  preliminary  survey 
of  the  road. 
(209)  The  Preliminary  Survey 

This  survey  is  under  the  direction  of  c.  chief  of  staff  who 
proceeds  to  set  out  a  series  of  straight  lines  of  varying  length 
following  the  route  already  determined  in  the  reconnaissance  survey. 
To  do  this  the  engineer  consults  always  the  notes,  maps,  and  indi- 
cated route  formerly  prepared,  making  such  changes  as  may  be 
necessitated  by  conditions  encountered.  The  passing  of  a  serious 
obstacle  or  the  choosing  of  a  more  advantageous  course  may  of  course 
necessitate  the  alteration  of  the  route  previously  selected,  but 


Surveying-IB.  Assignment  £,  page  5. 

such  alteration  should  not  be  made  for  light  or  transient  reasons. 
All  date,  of  the  reconnaissance  survey  are,  however,  subject  to 
liberal  interpretation,  and  a  line  may  be  made  to  deflect  left  in- 
stead of  right  or  be  terminated  or  prolonged  to  suit  the  careful 
exercise  of  judgment  on  the  part  of  the  chief  carrying  out  this 
preliminary  survey.   Lines  and  grades  actually  laid  out  in  the  pre- 
liminary survey  are  not  hard  and  fast  lines,  for  they  may  themselves 
be  revised  when  the  location  is  in  progress;  but  the  preliminary 
survey  should  in  the  main  be  conducted  very  much  as  though  such 
were  the  case.  The  preliminary  line  is  therefore  staked  out  upon 
the  ground.  An  accurate  map  to  scale  and  a  set  of  notes  complete 
in  every  detail  are  made  which,  of  course,  must  be  in  perfect 
agreement. 

The  preliminary  survey  parties  are  three,  all  under  the  di- 
rection of  the  chief  engineer.  They  consist  of  a  transit  party,  a 
level  party,  and  a  topographic  party.  In  the  first  are  required  a 
transit  man,  two  rodmen,  an  axe-man,  and  a  stake-man.  In  case  the 
compass  is  used  instead  of  the  transit  the  rear  rodman  may  be  dis- 
pensed with.  The  instrument  man  of  course  handles  the  transit  (or 
compass)  and  conducts  the  work  of  his  party  under  the  general  di- 
rection of  the  ehief  of  staff.  The  level  party  is  composed  of  a 
level-man  and  one  or  two  rodmen  who  follow  the  transit  party  as 
closely  as  possible  and  at  the  close  of  the  d?.y  are  perhaps  only  a 
few  rods  in  rear  of  the  transit  party.  One  or  two  topographers  can 
take  care  of  their  portion  of  the  work,  but  the  topographers  should 
keep  well  up  also  with  the  levelers,  and  transit  party,  as  it  is 


Surveying-IB.     Assignment  28,  pr.ge  6. 

necessary  frequently  to  procure  requisite  data  from  these  other 
parties. 

Having  exactly  determined  the  point  of  beginning  of  the  road 
about  to  be  projected,  the  chief  of  staff  establishes  this  point  by 
setting  a  permanent  monument  of  suitable  character.  The  latitude 
and  longitude  of  this  point  is  carefully  determined  by  astronomical 
observations,  these  being  entered  in  the  notes  of  the  preliminary 
survey.  The  point  is  also  tied  to  two,  or  better,  three  fixed  land 
marks  of  more  or  less  permanent  character,  the  bearing  and  distance 
of  which  are  likewise  recorded.  This  point  is  designated  as  the 
zero  point  of  the  line  and  is  referred  to  as  0+QO  (zero  plus 
naught  naught). 

The  subsequent  stations,  successively  100,  200,  300  feet 
distant  and  so  forth,  on  the  final  "location"  are  then  designated 
1+00,  2  +  00,  3  +  00,  etc.;  other  points  on  the  line  are  called 
pluses,  as  at  B,  1+60;  at  c,  3  +40;  etc. 

(210)  For  purposes  of  illustration  the  manner  of  ranging  out  a  railroad 
is  given  in  Figure  80  given  on  the  following  page. 

Beginning  at  station  0  +00,  the  latitude  and  longitude  of  the 
station  having  been  determined  and  the  point  tied  to  a  permanent 
fixed  point  by  bearing  and  distance,  the  line  is  ranged  N  11°  30'  ¥ 
160  ft.;  then  the  line  deflects  to  right  30°  00"  to  a  point  340  ft. 
from  point  of  beginning;  thence  42°  00'  L  to  567  ft.;  then  65°  00' 
R  to  775  ft.;  thence  26°  10'  R  to  1000  ft.  (The  distances  are  made 
quite  short  to  condense  the  diagram,  but  the  principle  is  the  same 


Surveying-IB.  Assignment  28,  page  7. 


Q+00 


Lei.  39*  i6>  u 
LOMQ.  /2/e  /4' w 


as  for  longer  tangents). 
The  full  stations  are 
marked  upon  the  line  as 
also  the  points  of  de- 
flection as  1+  60,  3  +  40, 
54-67,  7  +  75,  and  these 
are  always  measured  from 
the  initial  point. 

(211)     The  instrument  used  in  the 
preliminary  survey  may  be  either  the 
compass  or  the  transit.  If  the  compass 
is  used  it  may  be  equipped  with  sight- 
ing standards  or  with  a  telescope  pro- 
vided with  cross  hairs  for  giving  the 
line  of  sight.  But  if  a  compass  is  em- 
ployed the  local  magnetic  attraction 
should  be  reckoned  with,  and  resort 
to  the  use  of  a  transit  may  prove  ad- 
visable. The  compass  on  the  pre- 
liminary survey  has  usually  been  con- 
sidered sufficiently  accurate,  while 
the  simplicity  of  reading  bearings  of 
the  tangents  has  brought  it  much  into 
favor . 

If  the  transit  is  used,  it  is 
sufficient  to  run  the  line  by  deflec- 
tion angles  as  shown  above,  Fig.  80. 


Surveying-IB.  Assignment  28,  paga  8. 

The  first  segment  of  the  line  is  ranged  out,  either  with  or  without 
the  use  of  the  transit;  the  transit  is  then  set  upoon  a  forward 
point  of  the  segment,  a  back  sight  with  telescope  inverted  is  taken 
upon  the  former  station,  the  telescope  inverted  to  normal  and  the 
line  continued  in  line  -with  the  rear  segment,  and  this  process  is 
continued  to  the  point  where  the  course  of  the  road  may  turn  to  the 
right  or  left  (i.e.,  deflect). 

Vifhea  the  point  of  deflection  is  reached  the  transit  is  set  up 
over  this  point,  the  upper  plate  is  claused  with  the  A  verneir  of 
0°,  and  trith  the  telescope  plunged  a  backward  sight  is  taken  to  any 
convenient  point  on  the  last  preceding  segment;  the  lower  plate  is 
now  claraped  and  the  telescope  is  then  turned  to  normal,  which  places 
the  line  of  sight  in  line  with  the  continuation  of  the  last  segment 
(or  tangent  of  the  road).   If  now  the  upper  plate  be  undamped  and 
a  sight  (forward)  be  taken  on  a  point  on  the  next  succeeding  tangent, 
the  vernier  plate  of  the  transit  -will  read  the  deflection  angle  at 
the  point  occupied. 

(213)      Note  keeping  on  the  preliminary  survey  is  of  especial  importance; 
all  data  that  can  in  any  way  contribute  to  clearness  in  determining 
the  next  important  step,  towit,  the  paper  location  of  the  road,  must 
be  gathered  in  systematic  arrangement  and  neat  form. 

Specimen  notes  are  shown  on  the  accompanying  sh3et. 

The  student  is  referred  to  Searles  «  Ives  Handbook  of  Field 
Practice  in  Railroad  Surveying. 


S'jrveyir  T,-1B< 


23,  page   9. 


Questions  to  Assignment   28 


1.  State  the  general  outline  of  work  of  the  chief  engineer  on  a 
railroad  reconnaissance    survey. 

2.  What  are  the  data  required  in  the  preliminary  survey? 
Define  deflection  angle,  tangent,  and  bearing. 

Notes   of  R.  R.  Preliminary  Survey 


Defl.    . 


61 

60 
59 
58 
57 
56 


8°57'R 


49°  13  'P. 


14°42'L 


Magnetic 


Ang. 


25°20'L 


9°00'R 


49eK>'R 


B  *  o  *      °        F • 3 


N48030'E 


N23°10'E 


W39030'E 


N  9°20'W 


14°40'L  !  II  4°55'E 


'iR.   81 


N48°30  'E 


H39°50  'E 


I-J  9°45'W 


Bearing  - 


N26°42'E 


N51°59'El    (Var.    3°29') 


N43°02  'E 


(Var.    3°12') 


N   6°linvi    (V^r.   3°54') 


Colo   Beof>n 


(N805i'Ejl 


Last 


« 
i 


56.3 


Uote :     The  notes  are  arranged  to  read  from  the   bottom  of  page  upward,   as   shown 
by  numbering  of   stations;   the  notes  here   given  are   a   coni.inua.tion  from  a 
preceding  page.      Sketch  on  the  right   gives  principal  data  to  assist   in 
mapping  the   "Preliminary"  and  also  the   "Paper   Location".      Important 
topographic  features  are  shovm,   but  minor   details   are   not  necessary,   and 
hence  are  omitted  from  sketch. 


UNI\5,KirfY  OF  Ci-LIFORKIA  SJCIENSIOK  DIVISION 

Correspondence     Courses 

Surveying  IE  Assignment  29  Swafford 

Railroad  Survey  ing,    -    Tangents  and   Curves 

Foreword 

In  this  assignment  £-n  extended  consideration,  of  the    simple 
curve  as  used   in  railrcad    surveys  will  oe  made.      The   student   is 
directed  to  the    latter  part   of  Assignment  26  v«here  the  use   of   the 
simple   curve   on  streets   in  City  Surveying  is  treated. 
(P13)   Xangents^anC   Curves 

A  line   cf  railroad    is  essentially  a  series   of   straight   lines, 
called   te.nge.ntr,    and  curves   -  the    latter   connecting  the  former   in 
continuous   sequence. 

In  the  preliminary    survey  a  succession  of  straight  lines  of 
varying   length  '.vhich  intersected  with  each  other   from  point  to 
point  along  the   route,  were    staked  out.      ±hs  roadbed  and  especially 
the  tracks  cov.id  not    02  cf   use   in  carrying  trains  o\er  such  a 
course,   end   it    oe comes  necessary  to  connect  the   straight  segments 
of  ro&c    &j    carves   of  vaiyirig  degree  of  curvature.      These  curves, 
circular   in  form,  are  :uacl  :•  tangent  to  tns  tv;o  lines   of  direction, 
and   are  c1:  aruitrery   radius   (or  degree). 

lor  eny  giver   angle    of  del lection  of  the    line,   the  degree 
of  the  curve   is  chosen,   usually  from  several  corns  iterations. 
Matters   influencing  the   choice   of  degree  cf    curve  are    :-  proximity 
to  other  curves,    or   distance   ap*rt  of  points   of  intersection 

•(deflection  vertices),   nature   of  grades   encountered  on   the    line 
cr    in  proximity  tc  the  curve,   nature   of  earth  materials   on  vhich 


Survey  ing  IB  Assignment  29  Page  2 

the  curve  is  to  be  constructed,  approaches  to  bridges  and  tunnels, 
even  the  procurement  of  right  of  way,  and  the  speed  of  trains 
operating  over  the  curve.   A  small  degree  of  curve  is  always  to 
be  sought,  all  things  consideree.  Beyond  such  matters  the  choice 
of  a  degree  cf  curve  is  rather  an  arbitrary  mattar  left  to  the 
judgment  of  the  engineer  in  charge.  The  simplicity  cf  the  com- 
putations should  not  oe  vholly  overlooked  in  the  selection; 
generally  the.  larger  the  deflection  of  the  taagents  (i.e.  the 
larger  the  intersection  angle)  the  smaller  the  degree  of  curve; 
hence,  the  more  gradual  the  curve  connecting  straight  lines. 

For  example,  if  the  intersection  cf  tangents  is  40°,  a  5° 
curve  would  give  3  chords  (or  hundred-foot  stations)  on  the  curve, 
while  a  10°  curve .would  give  out  four  stations.  The  former  -would 
permit  trains  to  move  at  a  speed  of  say  40  miles  per  hour,  the 
latter  at,  only  25  miles  per  hour.   In  addition  the  work  done  en 
the  former  would  oe  much  less,  the  wear  on  ro^doed  and  rails,  as 
also  the  v.ear  on  rolling  stock  would  alsc  oe  less  for  the  5°  curve 
than  for  the  10°  curve. 

Referring  tc  Fig.  S2,  AQ  and  Mb  are  tangents  intersecting 
at  k-   QMB  is  the  intersection  an6le  I  (=  Central  angle  C).   If 
nov  a  curve  AN3  is  laid  out  tangent  to  AQ,  at  ^  ana  to  Mi  at  B, 
All  and  Mb  are  called  the  tangent  distances  from  the  points  of 
intersection  (p. I.);  A  is  the  point  of  curve  (P.O.)  and  3  is  the 
point  of  tangent  (F.T.).  Radii  from  P.O.  and  p.  I,  meet  at  C,  the 
center  of  curvature.   C  is  the  central  angle. 


Surveying 


29 


Page     3 


F.I. 


Fig.      82 

The   chord    of    the   curve   joining  ?.  C.    s.ad   P.  T.    is  called 
the    long  chord.      ihe   distance  fron  the   .Tad-point   of  the   long  chord 
to  the   midpoint   of  the   curve    IE    called  the   middle    ordinate ;     the 
distance  MN  from  the  miipoint   of  the  curve  to  the   point  of   inter- 
section of  the   tangents    is   the   ex-secant   (i.e.    the   external   seg- 
ment  of  the    secant),   C.M. ,    called  the   external   distance. 

Ihe   mathematical    relations   of  these    lines  and   angles  are 
expressed   ceo*KtricaI3.y,    or   trigonometrically .    as  folloivg; 

The  angle  C    is  equal  to  angle    1.      I  is  the   supplement   of 
angle  AMD   and   angle *AM6    is   supplemental   to  angle  C;   hence   C  =   I. 


Surveying  IB 


Assignment  29 


Page     4 


Augle   IL-'JJ    (or  MBA)    is  equal    to  one-half  of  angle    I.      Angle    I 
is  equal  to  angle  L,   plus  angle  B,    and  angle  A  equals  angle  3; 
hence  angle  A  -  g-,  angle  B  =  -^ . 

Tangent  Distance   is  equal  to  radius   of  the  curve  multiplied 
by  the  tangent  of  ons-haif  angle  C   (or  or.s   half  angle    I). 
AJs  =  AC  tan  C/2. 

Long  chord   is  equal  to  twice  the   product  of  the  radius  of 
the  curve   into  the   eine  of  one  half  C.        L.  C.    =  2R  sin  C/2. 
(Since  C  -  I,    I  ma»   be   substituted  for  C    in  the    last  tv/o  formulae.) 

The  middle   t-rdinate    is   equal  to  the  radius  diminished  by 
the  radius   into  the  cosine   of  one  half  C   (  =  — ).        Mid.    Ord.   = 
R  -  R  cos  •£  ,    which  reduces  to  Mid.    Ord  =  R   (1  -  cos  — )  =  R  vers  — . 

The  external  distance   is  equal  to  the  square   root  of  the 
tangent   squared  plus  the   radius  squared  diminished   by  the  radius. 


Ex-    Dist.    r  A/Tan2  t-  R2/  -  R 

The   degree  of  curve   is  defined  as  the  angle  at  the  center 
(or   its   arc)    subtended    by  a  chord   of  lOu  ft. 

In  Fig.    83,   AB,    a 


chord  of  100  ft.  subtends 
the  angle  at.  C,  or  arc  AmB ; 
AC  and  BC  are  radii  of  this 
arc;  by  trigonometry: 
A3  :  AD  ::  2  sin  D/2  :  r, 
r  being  the  radius  of  unit 
circle  .  AB  is 

100. 


Surveying  IB  Assignuent  29  Fage  5 

Substituting  10Q&  =  *  S*n     ;  dividing  by  2,  50/R  =  sin  D/2; 

solving  for  R,  R  =  . 5Q  ,  . 

sin  D/2 

There  will  be  as  many  chords  of  100  ft.  in  the  curve,  P.  C. 
to  P.  T.  as  the  degree  of  curve  is  contained  times  in  the  central 
angle.   This  may  be  expressed  by  the  equation  N  =  ^  (=  ^-),  where 
N  is  the  number  of  100  foot  chords  in  the  curve,  I  is  the  inter- 
section angle,  and  D  is  the  degree  of  curve. 

The  number  of  chords  are,  therefore,  inversely  proportional 
to  the  degree  of  curve;  therefore  the  length  of  the  curve  from 
P.O.  to  P.  T.  ,  the  tangent  distance,  and  the  radius  of  the  curve 
increase  as  the  degree  of  curve  decreases.   It  follows  then,  that 
as  the  degree  of  curve  for  any  given  intersection  angle  diminishes 
the  flatter  the  curve  becomes  (or  more  nearly  approaches  a  straight 
line). 

The  character  of  curve  may  be  readily  determined,  therefore, 
by  the  number  of  stations  on  the  curve;  the  radius  of  the  curve, 
the  tangent  distance,  the  length  of  the  curve  (from  P.C.  to  P.T.  ), 
ant?  the  long  chord  increase  with  the  number  or  stations  (i.e.  the 
number  of  chords)  and  therefore  inversely  as  the  degree  of  curve. 

It  is  the  c cam on  practice  to  choose  the  degree  of  curve, 
as  that  for  any  given  intersection  angle  determines  the  other 
elements  of  the  curve.   Soaie  engineers  choose  a  radius  of  curva- 
ture; and  in  some  special  cases  it  is  expedient  to  assume  the 
tangent  distance,  as  the  point  of  oeginning  of  the  curve  or  its 
relation  to  bridges,  tunnels,  etc.,  may  make  it  desiraole  that 
the  curve  should  oegin  or  end  at  a  definite  point. 


Surveying  IB 


Assignment  2£ 


Puge     6 


(214)   T!he  Deflection  Angle 

This   is   the   angle  which  the  chord  naices  v;ith  the   tangent  and 
is  equal  to  one-half  the    intersection  angle   divided    ty   the  numoer 
of  chores   in  the  curve.      In  r'ig.    84  is   shown  a  curve   of  four  sta- 
tions  (each  100  ft.). 

The  angle  BAM,  which 
is  the  angle   formed  by 
the    long  chord  and  the 
tangent,    is  equal  to  one 
half  I.     W.&,   MAb,   MAC, 
MAC,   are  the  departures 
of  the    lines  Aa,   Ab,   Ac, 
Ad,    from  the   tangent  AM- 
The  deflection  angle   is 
here    1/2   *  n;     since  n 


Figure  84 


in  this  case  is  *,  then 
tne  deflection  a^le  is 


1/4  cf  1/2  (=  ]£r  -  I)-   J-'he  Deflection  angle  is  used  in  setting 

off  the  curve  in  the  field.   A  transit  is  set  ap  at  P.C.  sighted 

Off 

on  ?.  I.  ;  the  deflection  is  then  turnedAon  the  limb  I/£n,  I/n, 

3I/2n,  21/n,  the  deflection  angle  aeing  added  successively  to 
each  preceding  angle - 
r!5)        We  give  in  the  following  pages  a  few  examples  to  illustrate 
end  shov  the  methods  of  computation  for  the  several  elements  of 
simple  curves. 


Surveying-13  Assignment   29  Page     7 

1.  Given  the  intersection  angle,  60°;  it  is  desired  to  lo- 
cate 5  full  stations  on  the  curve  which  begins  at  the  P. C.   What  is 
the  degree  of  curve? 

Solution:  N  =  I/D 
D  =  I/N 
D  =  60%  =  12°  ans. 

2.  If  the  intersection  angle  is  60°,  the  degree  of  curve  6°, 
what  will  be  the  length  of  the  curve? 

Solution:  Length  =  100N 
N  =  I/D 

N  =  60/6  =  10 

• 

.  .  Length  =  100  x  10  =  1000  ft.  ans. 

3.  The  intersection  angle  is  70°;  find  the  radius  of  a  5° 
curve  and  the  number  of  chords  in  the  curve. 

R  =  50/sin  £ 
2 

=  50  *  sin  2°  30" 

=  50  *  0.04362  =  1146.28  ft.  ans. 

4.  In  the  above  example  what  is  the  tangent  distance? 

Tan.  Dist.  =  R.  tan  1/2 

=  1146.28  x  tan.  35* 

=  1146.28  x  0.70021  =  902.64  ft.  ans.  ) 

5.  For  the  same  intersection  angle  and  degree  of  curve  what 
is   (a)  the  number  of  full  stations  on  the  curve?  (b)  the  deflec- 
tion angle?  (c)  the  long  chord? 

(a)  N  =  I/D 

=  70°/5°  =  14  ans. 

(b)  d  =  1/2 

N 

=  I/2N 
=  70°/28  =  2°  3C1  ans. 


Surveying-IB  Assignment  29  Page  8 


(c)  L.C.  =  2R.  sin  1/2 

=  2  x  1146.28  x  sin  35° 

=  2  x  1146.28  x  0.57358  =  1314.97  ans. 

The  last  solution  is  conveniently  made  by  use  of  logarithms 

log  2  =  0.30103 
"  1146.28  =  3.05929 
"  sin  35°  =  9. 75859-10 

11     Product  =13.11891-10   .*.    anti-log  =  1314,94     ans. 
6.     The  external  distance   (a)   and   the  middle   ordinate   (b) 
may  also  be  computed  for  the   same  curve. 

(a)     Ex.   Dist.  =      y/tan2  4-  R2     -  R 


1146. 282   -  1146.28 


=       644230.  9695  +   1314957.8384       -   1146.28 
=  1399.71   -   1146.28  =  253.43  ft.      ans. 

(b)  Mid.  Ord.  =  R  (1  -  cos  1/2) 

=  1146.28  (1  -  cos  35°) 
=  1146.28  (1  -  0.81915} 
=  1146.28  x  0.18085  =  207.30  ft.  Ans. 

(216)  Sub -Chorda 

In  general  a  chord  of  a  curve  is  understood  to  be  100  ft.  in 
length,  and  the  foregoing  consideration  of  the  simple  curve  was  made 
on  this  assumption.  When  a  chord  of  less  than  100  feet  is  taken  as 

an  element  of  the  curve  it  is  called  a  suo-chord.   The  sub-chord  may 



be  nominally  50  feet,  25  feet,  or  any  fractional  part  of  the  100  ft. 

chord;  but  its  actual  length  is  slightly  more  than  its  nominal  length, 
since  in  measuring  upon  the  arc  of  the  curve  it  is  evident  that  two 
50-foot  chords  are  not  equivalent  to  the  two  chords  of  any  arc  sub- 
tended by  a  100  foot  chord.   Shown  in  Figure  85. 


Survey ing -IB 


Assignment  29 


Page  9 


The  deflection  for  a 
sab-chord  is  one  half  its 
subtended  arc.  Therefore, 
if  1  is  the  length  of  a  sub- 
chord  and  d1  is  the  central 
angle  subtended  by  1,  then 
1  =  2(R  sin  d'/2).   Since  R  = 


50 


we  have  by  sub- 


Fig.  85. 


sin  D/2 

stituting  this  value  for  R  in 


1  = 


1  - 


100 


sin  D/2 

100  sin  d'/2 


the  above  equation: 
x  sin  d '/2;  or 


whence 


sin  D/2 
sin  d'/2  =  1/100  sin  D/2 

Since  in  the  case  of  small  arcs  the  sine  is  approximately  equal  to 
the  arc,  when  the  arc  D  is  not  greater  than  8°  or  10°,  the  error  in 
such  assumption  (sine  =  arc)  is  negligible,  and  we  may  write  this 

formula,  thus: 

d'/2  =  1/100  x  d/2,  or  more  simply 

d1  =  1/100  D;  whence 
1  =  100  d'/D 

by  proportion  1  :  100  ::  d1  :  D;  or  we  say  the  length  of  the  sub- 
chord  is  proportional  to  the  arc. 

Of  course  for  arcs  greater  than  10°  the  error  of  the  fore- 
going assumption  must  be  reckoned  with. 


Surveying-IB  Assignment   29  Page  10 

In  the  figure   (fig.   85),    it  is  evident  that  a  correction  must 
be  added  to  a   sub-chord  of  nominal  length  to  give  the   length  neces- 
sary for   say  two  50  foot  sub-chords  to  reach  a  point  on  the  curve 
also  reached  by  a  chord  of  100  feet  from  the  same   initial  point. 

Should   it  be  required  to  use  a  50  foot  tape   in  setting  out  a 
curve,   then  the  distance   should  be  determined   oy   formula  given  above 
and   this    length  used   in  the  v.'ork, 
(217)     Example: 

To   lay  out  a   15°  curve  with  a  50  foot  tape,  7.'hat  correction 
must  be  added  to  the  tape? 

Here  D  =  15°,   D/2  =  7°30'    and   o'/£  =   1/iCO  x  D/2 

d'/2  =  50/100  x  7°   30'   =  3°  45' 
100  x   sin  3°   45'        100  x  0.0654 


0.1305 
(The  answer   is  carried  to  the  third  decimal  place  for   illustration 

only.) 

When  a  curve  begins  with  a  sub-chord,  as   in  the  case  where 
the  P.O.    does  not  fall  at  a  full  station  but  at  some  distance  be- 
yond called  a  plus,    for   example:     P.O.    falls  at  29  +  35  ft.,   this 
nominal  length  of  sub-chord  must   De    increased;   thus  the  nominal 

length  of  this 
sub-chord   is  then 
100  -   35  =  65  ft. 
If  the   degree   of 
curve    in  this 


Surveying-IB  Assignment  29  Page   11 

case  is  14°,  then  D/2  =  7°  00';  d'/2  =  65/100  x  7°00'  =  4955  or  4°3S'; 

100  x  sin  4°  33'  _  100  x  0.0793  ,  Ty, 

therefore,  1  =  -  =  65.093.   (In 

sin  7°  00'  0.1219 

setting  out  this  curve  the  measurement   is  carried  to  the   hundredth 

foot   only,    i.e.,    1  =  65.09  ft.) 

The   location  of  curves,   their  mapping,   etc.,  will  be  treated 
in  Assignment  30. 

Reference   is  made  to  Searles  &  Ives,   Field  Engineering,   pp. 
44-60. 

Problem  to  Accompany  Assignment  29 

Problem: 

At  a  point  375.8  feet  from  station  237  on  a  line  of  road  the 
deflection  is  36°  00'  R.  Find  the  elements  of  a  six  degree  curve. 

(Find  number  of  chords,  length  of  sub-chords  both  nominal  and 
corrected  length,  radius  of  the  curve,  tangent  distances,  the  plus 
to  P.C.,  at  P.T.,  long  chord,  middle  ordinate,  and  the  external 
distance.) 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 

Correspondence     Courses 
Surveying-IB  Assignment   30  Mr.    Stafford 

Mapping,  Location,  Gracing. 
The  Flanimeter  and  Its  Use. 

Foreword 

.Methods  of  plotting  of  points,  lines,  and  details,  and  also 
the  locating  of  railroad  lines  both  on  paper  (the  paper  location) 
and  in  the  field  ere  treated  in  this  assignment.  A  descriptiqp  of 
the  planiaieter  anc  its  use  in  measuring  areas  of  maps,  diagrams, 
etc.  will  s.lso  receive  attention. 
(213)       A  map  is  a  pictorial  representation  of  a  oortion  of  land  or 

•.vater  surface.   It  may  range  from  the  simplest  outline  or  sketch  to 
the  finished  picture.,  riving  details  of  houses,  -wails,  fences,  and 
other  salient  features.   Generally,  in  surveying,  it  is  a  represen- 
tation to  a  given  scsle  of  the  angles,  lines,  streams  or  other 
bodies  of  v,-ater,  ridges,  valleys,  and  slopes  vhich  have  been  secured 
by  surveying  methods  and  are  emoodied  in  suitaole  records  called 
notes  of  the  survey. 

In  order  to  make  a  map  it  is  necessary  to  have  notes  or  record 
of  a  more  or  less  complete  character.   The  completeness  of  the  map 
•will  depend  upon  the  amplitude  or  scope  of  the  data  contained  in  the 
notes.   It  has  already  been  made  clear  that  notes  should  omit  no  de- 
tail in  the  \~&j  of  data  that  can  materially  assist  in  producing  an 
effective  map.   There  should  oe  locations  and  measurements  of  points, 


Survey ing -IB  Assignment  30  Page  2 

lines,  and  angles  an<^  their  relative  positions  together  with  ample 
descriptions.  These  are  often  best  shown  oy  naming,  numbering,  and 
picturing  in  proper  skstches. 

A  line  is  shown  in  length  (to  scale)  and  angle  (bearing,  de- 
flection, etc.). 

An  angle  is  represented  in  its  true  magnitude  in  units  of 
circular  arc  (known  as  "angle"). 

Elevations  and  depressions,  slopes,  valleys,  and  hills  are 
indicated  oy  conventions  called  hatchings  or  contours.   Streams  are 
shown  by  the  lines  that  picture  irregular  water  courses  as  they 
occur  at  lov;esr  valley  lines  or  "thalwegs"  (a  German  word  meaning 
"vs lleyways") .   The  convention  for  streams  calls  for  lines  that  are 
very  fine  near  the  source  and  that  gradually  increase  in  width  to- 
ward the  mouth  or  point  of  discharge;  in  larger  streams  where  the 
scale  permits,  two  lines  representing  the  banks  of  such  water 
courses  are  employed  in  the  representation. 

Lines,  when  straight,  are  drawn  qy  means  of  a  ruler  (straight 
edge,  T-square,  triangle);  when  curved,  by  use  of  the  compass  or  a 
curved  ruler;  when  irregular,  as  meander  lines,  profiles,  etc.  Dy 
short  straight  free-hand  lines  from  point  to  point  as  previously 
determined. 

Angles  are  set  off  oy  one  of  three  principal  methods;  by 
tangents,  by  chords,  or  by  protractor.   These  three  methods  are  il- 
lustrated in  the  following  figures  and  concrete  examples,  by  which 
angles  of  bearing,  deflection,  or  included  angle  are  set  off  or 
mapped. 


Surveying-IB 


As  s  ignme  nt  50 


Page  3 


(219)  Tangent  Method 

To  set  off  an  angle  of  bearing  by  the  tangent  method, 

measure  a  distance  from  the  vertex  of  say 
ten  inches  along  the  meridian;  from  a 
table  of  natural  tangents  take  the  tangent 
of  the  bearing  which  should  be  multiplied 
Dy  10.  Upon  the  perpendicular  drawn  to 
the  meridian  of  ten  inches,  lay  off  this 
distance  (10  x  tan.  of  bearing);  through 
the  points  thus  determined  draw  the  re- 
quired line  which  will  make  the  required 
angle  tne  meridian. 

Example:   On  a  scale  of  1  inch  equal  200  feet  draw  a  line 
750  ft.  long,  having  a  bearing  N  38°  40'  E.   Here  SN  represents 

the  meridian  and  the 
required  line  has  its 
origin  at  A.  Lay  off 
10  in.  along  SN  from 
A,  giving  the  point  m. 
Erect  a  perpendicular 
mn  equal  to  10  x  tan- 
gent (natural)  of 

38°  40'  (10  x  0.8CO  =  8.0).   Through  An  draw  the  line  AB  making  this 
750  ft  (by  scale  .".75  inches).   For  convenience,  construction  lines 
have  been  drawn  to  a  scale  of  3/16  =  1' . 


Survey ing -13 


Assignment  20 


Page  4 


Since  the  tangents  of  angles  over  45°  are  greater  than  one  and 
the  tangent  increases  rapidly,  reaching  infinity  at  90°,  for  angles 
greater  than  50°  it  is  better  to  use  the  cotangent  instead  of  the 

tangent.  To  illustrate:  Lay  off  a  line  that  deflects  78°  41'  R  by 

i 

use   of  the  cotangent  as 

shown  in  Fig.    89.      In  this 
case  through  the  vertex  A 
dra-w  AL  perpendicular  to 
thfc   directed   line  AM;   lay 
off  10  in.    on  AL  (=  Am) ; 
at  m  erect  the  perpendicular 
an  making  ran  =  10  x  cot  78° 41' 
(10  x  0.200  =  ?);        now  draw 
AB_  from  A  through  n.     The 
angls  MAE    is  the   required 
angle.     Had   it  been  attempted 


? 


(jc  sea , 

to  set  up  the  tangent   of  78°  41'  at  M  it  would  have  required  a   line 
10  x  -±.99695  inches   long  or  nearly  50  inches,  much  beyond  the   limits 
of  the   ordinary  drafting   oo?rd. 

The  tangent  method    is   especially  applicaolt   and   convenient   in 
plotting  open  traverses  such  as  are  made   in  road  and  railroad   surveys. 
A  study   of  Fig.    90  will  sufficiently   illustrate   this  method. 


Surveying-IB 


Assignment  30 


Page  5 


oc 


In  general  the  angles  here  are  small  and  of  course  the  tangent 
is  properly  used;  but  at  station  17  •*•  05  the  deflection  angle  being 
59°  15'  R  the  cotangent  is  more  conveniently  applied. 
20)  The  Chord  Method 

The  chord  of  an  arc  is  the  line  joining  the  extremities  of 
the  arc.  Tables  are  sometimes,  out  not  commonly,  included  in  the 
tables  of  engineering  handbooks.  Referring  to  Fig.  91  it  will  be 
seen  that  the  chord  of  any  arc  of  unit  circle  is  equal  to  twice  the 

sine  of  one -ha If  the  angle  : 
In  the  unit  circle  Radius  r 

1;  sin  angle  6  =  —-=^2.- 
Ga   1 

c.ngle  6ab  =  2  angle  aQc 
and   ac   =  cb  or  ab  =  2ac  ; 
i.e.,   chord  ab  s  2  sin 
angle  a6c.      Now  in  A6B, 
the  arc  A>3    subtends  the   same  angle  6  and  the  chord  Afl ;    by  similar 


Surveying-IB  Assignment  30  Page  6 

triangles  da  :  8A  =  ab  :  AB  ;  but  6a  =  Radius  =  1,  and  ab_  =  2  sin 
92;  .".  1  :  6A  =  2  sin  angle  6/2  :  £3 ;  and  AB  =  6A  x  2  sin  angle 
6/2. 

If  in  a  special  application  of  this  method  we  make  the  radius 
of  the  construction  arc  5  inches  long,  then  the  chord  is  equal  to 
10  x  sin  0/2.  That  is,  for  any  given  angle,  take  the  natural  sine 
of  half  this  angle,  move  the  decimal  point  one  place  to  the  right 
and  lay  this  off  as  the  chord  to  a  radius  of  5  inches. 

In  plotting,  describe  the  arc  and  from  the  point  where  it 
cuts  the  line  of  direction  scale  off  the  straight  line,  10  x  sin 
6/2,  with  the  proper  scale;  draw  the  required  line  through  the 
point  thus  found. 

This  method  is  applicable  to  plotting  of  any  sort  and  when 
tables  of  chords  are  available  is  very  satisfactory  and  simple. 
It  is  especially  applicaole  to  plotting  of  interior  angles.  Where 
the  angle  is  large,  exceeding  70°,  it  is  better  to  use  complementary 
construction,  using  sine  of  half  the  complement  of  the  required  angle. 
(221)  protractor  Method 

The  protractor  is  a  universal  instrument  for  plotting  and 
measuring  angles  of  any  sort,  such  as  bearings,  deflections,  or 
azimuths.  The  protractor  is  made  of  various  kinds  of  materials,  as 
paper,  brass,  celluloid,  silver,  etc.,  and  of  sizes  and  styles  suited 
to  the  various  needs  of  mapping.  Exquisite  instruments  made  of 
silver  with  accurate  and  small  subdivisions  and  supplied  with  verniers, 
are  to  be  had  from  the  instrument  makers,  and  the  map  draftsman  will 


Surveying-IB  Assignment  30  Page  7 

find  use  for  these  where  great  accuracy  and  many  angles  are  to  be 
laid  out.  A  good  plain  protractor  is  usually  all  that  is  required, 
aad  in  work  of  some  kinds  a  large  paper  protractor  is  sufficient 
and  convenient.   Such  paper  protractors  may  oe  purchased  in  several 
sizes,  8  inches  and  14  inches  diameter  being,  common  sizes.  The 
larger  size  is  divided  into  1/4  degree  divisions;  to  set  off  angles 
closer  than  15  minutes  of  arc  it  is  possible  to  estimate  smaller 
units  as  7.5  minutes  cr  even  5  minutes.   This  is  usually  within  the 
required  limits  of  accuracy  in  construction  but  where  higher  ac- 
curacy is  desired,  the  tangent  method  should  oe  used. 

Generally  it  is  convenient  to  have  the  protractor  in  semi- 
circular form;  it  is  so  used  that  the  center  of  the  circle  is 
placed  at  the  vertex  oi  the  angle  to  oe  plotted  with  the  diameter 
of  the  protractor  along  the  meridian  or  directed  line,  the  angle  in 
degrees  and  fractions  may  then  oe  set  off  oy  the  pencil  point  or 
pricker  and  the  line  drawn  through  the  points  thus  determined,  A 
protractor  of  semi-circular  form  may  be  conveniently  used  against 
a  straight  edge  or  T-square  placed  along  the  meridian;  the  center 
at  the  angle  vertex. 

For  plotting  azimuths,  especially  when  it  is  requirec  to  locate 
many  points,  as  on  detail  or  topographic  maps,  -^here  the  location 
is  shown  in  the  notes  by  azimuth  and  distance,  the  full  circular 
protractor  is  most  convenient.  For  such  use,  cut  out  the  protractor 
in  the  form  shewn  in  Fig.  92.  This  may  oe  done  with  a  sharp  knife 
along  fine  pencil  lines  previously  drawn  in  the  following  manner: 


Survey  ing- IB 


Assignment   3<j 


Page  8 


ADout  the  center  (accurately 
determined  by  intersections 
through  the  quadrantal  points), 
describe  a  circle  just  out- 
side (1/16"  or  1/8")  of  the 
graduated  circle.  Another 
circle  aoout  7/8"  inside  is 
then  drawn,  and  a  tongue 
about  2"  wide,  provided  to 

preserve  the  "center",  is  shaped  as  shown;  cut  out  carefully  to 
the  lines,  removing  the  U-shaped  portion  to  allow  lines  to  be  drawn 
or  seen  within  the  graduated  circle. 

New,  if  azimuths  are  reckoned  from  the  south,  put  the  center 
upon  the  point  about  which  azi-nuths  are  measured.   Place  the  zero 
of  the  protractor  (numbered  as  in  the  figure)  at  the  south,  and 
azimuths  are  then  determined  by  the  protractor  scale.   The  tongue 
may  be  folded,  so  that  the  space  v.dthin  the  entire  circle  is  open 
and  unobstructed  in  drawing  lines  in  that  portion  cf  the  map.   Other 
•ways  of  cutting  out  the  protractor  may  oe  used,  but  this  form  is 
found  to  be  very  convenient. 
(222)  Method  _of  Plotting  b_y  Co-ordinates 

A  map,  field,  or  open  traverse  is  often  conveninetly  and  ac- 
curately plotted  ay  means  of  coordinates.   The  coordinates  may  be 
simple  latitudes  and  departures  or  the  Cartesian  coordinates,  the 
latter  usually  obtained  from  the  latitudes  and  departures.   The 


Survey ing -IB 


Assignment  30 


Page  9 


origin  of  coordinates  is  in  most  cases  taken  at  the  lower  left  hand 
corner  of  the  sheet  and  so  chosen  that  the  most  westerly  point 
shall  be  upon  the  Y  axis,  the  most  southerly  point  upon  the  X  axis. 
By  this  method  the  ordinate  of  any  point  is  the  total  latitude  and 
the  abscissa  the  total  departure  reckoned  from  the  south  and  west, 
respectively. 

By  means  of  a  Toquare  and  scale  the  locations  of  abscissae 
are  rapidly  made ;  the  set-square  or  triangle  and  scale  are  similar- 
ly used  for  locating  ordinate  distances. 

Before  converting  latitudes  and  departures  to  coordinates 
they  should  De  carefully  adjusted  or  balanced  for  accuracy  in  plot- 
ting.  A  small  error  of  closure  gives  a  fair  indication  of  the  pre- 
cision of  the  mapping  and  this  error  should  fall  well  within  the 
required  limit  of  accuracy. 

The  coordinate  method  of  plotting  is  ooth  accurate  and  rapid. 
Since  the  work  of  computation  of  the  coordinates  themselves  is  the 
important  part,  this  should  Qe  done  carefully,  applying  the  usual 
checks. 

The  actual 
plotting  is  accom- 
plished by  means  of 
scale  and  T-square. 
Fig.  93  illustrates 
the  method  of  plot- 
ting by  coordinates. 


Pio. 


Surveying-IB  Assignment  30  Page  10 

Here  the  axes  of  coordinates  are  made  to  pass  through  the  most 
southerly  and  most  westerly  points  of  the  traverse;  hence  ay  the 
ordinate  of  A  is  found  on  the  Y  axis;  ax,  the  abscissa  of  A  is  zero; 
so  the  abscissa  of  B  is  bx  measured  along,  the  X  axis,  _by  falling  at 
the  origin.  C  is  located  ay  scaling  the  ordinate  £y  on  the  Y  axis, 
Cx  on  the  X  axis,  and  Oy  lines  perpendicular  to  the  tv;o  axes  at  £y 
and  Cx  respectively.  The  point  C  is  determined  by  their  intersec- 
tion.  It  should  be  noted  that  the  coordinate  axes  should  be  at 
right  angles  to  each  other,  and  if  the  T-square  is  used  to  draw  the 
lines,  as  dyD  and  dxD,  the  edges  of  the  drawing  board  should  be  like- 
wise square.   If  this  condition  cannot  oe  secured  it  is  preferred 
to  use  a  triangle  or  set-square  for  drawing  one  set  of  lines. 

The  plotting  of  details  within  any  traverse  or  triangulation 
scheme  is  best  done  Dy  angle  (bearing  or  azimuth)  and  distance. 
E23)  Final  Location  _of  Railway 

In  mapping  a.  final  location  of  a  railroad  the  tangents  are 
drawn  from  intersection  to  intersection  and  the  P.C.  and  P.T.  of 
any  curve  are  located  by  tangent  distance  from  the  P.I.   Arcs  of 
radius  equal  to  the  radius  of  the  curve  e.re  then  drarn  from  P.C. 
and  P.T.  and  their  intersection  becomes  the  center  of  the  arc  of  the 
curve  v-hich  is  then  drawn.  The  intersection  angles  are  best  laid 
off  by  the  tangent  method  of  construction.  3y  reference  to  Fig. 94 
this  method  may  be  readily  understood.  The  line  haveing  been  carried 
to  P.  I. ,  the  intersection  of  angle  I  is  constructed  fay  ths  tangent 
method.  Then  from  P.I.  the  tangent  distances  to  P.C.  anc)  P.T.  are 


Surveying-IB 


Assignment  30 


Page  11 


measured  off.  With  P.  C. 
and  P.  I.  as  centers  de- 
scribe arcs  of  radius 
equal  to  the  degree  of 
curve  intersecting  at  C« 
Then  with  the  same  radius 
and  C  as  center  describe 
the  curve  P.O.  to  P. T. 
(224)  Areas 

In  general  areas  are 
computed  directly  from 
data  procured  in  the  sur- 
vey; as,  v/hen  a  field  is 
surveyed  by  measuring  the 

triangles  composing  it,  or  oy  bearing  and  distance  from  \vhich  we 
pass  to  the  method  of  latitudes,  departures,  and  double  meridian 
distances,  etc.   Maps  plotted  to  scale  are  sometimes  drav»n  on  co- 
ordinate paper  and  the  area  thus  measured,,  But  if  a  map  has  been 
carefully  drav;n  to  scale  the  area  of  the  map  of  any  portion  may 
conveniently  and  rapidly  be  determined  by  the  means  of  an  instrument 
called  the  planimeter. 
(225)  The  Planimeter 

In  its  simple  form  the  planinetsr  consists  of  two  radial  arms 
hinged  together;  one  -rm  carries  a  wheel  turning  upon  an  axle,  the 
center  line  of  \vhich  is  parallel  to  this  arm,  v;hich  has  at  its 


Survey ing -IB 


Assignment  3C 


Page  12 


extremity  a  tracing  point  that  is  made  to  follow  the  bounding  line 
of  the  figure  whose  area  it  is  desired  to  measure.   The  extremity 
of  the  other  arm  has  a  point,  called  the  anchor  point,  Dy  means  of 
which  this  part  of  the  instrument  may  oe  fixed  to  the  surface  of 
the  diagram. 

Figure  95  shows  a  common  form  of  the  planimeter,  named  from 

its  inventor 
the  Amsler  plani- 
meter. K  is  the 
arm  to  which  the 
anchor  point  A 
is  attached;  h 

is  the  arm  be^riig  the  tracer  point,  ^>  These  two  arms  are  hinged 
at  J  and  are  so  shaped  near  the  hinge  that  the/  may  be  folded  to- 
gether about  the  wheel  W.  The  axis  of  W  is  made  parallel  to  the 
arm  h,  and  upon  the  axle  is  usually  a  v.onn  gear  that  operates  a 
disk  for  counting  the  revolutions  of  the  wheel.  The  wheel  is  sub- 
divided into  10  numbered  divisions,  each  of  v;hich  is  again  sub- 
divided into  10  equal  parts.  A  vernier  is  attached  to  secure  a 
reading  to  one-tenth  of  these  smallest  divisions.  The  counting 
device  consists  of  the  disk  that  gives  the  whole  number  of  revo- 
lutions of  the  wheel,  the  numbered  divisions  on  the  wheel  give  the 
10th,  the  smaller  subdivisions  show  the  hundredths  of  revolutions, 
and  the  vernier  gives  the  thousandths.   Figure  96  shov.s  a  reading 
of  4.516  -  4  is  taken  from  the  disk  C,  5  from  the  numbering  on  the 


Surveying-13 


Assignment   30 


Page  13 


FlQ.96. 


v.-heel,  1  (the  vernier  zero 
has  passed  this  point),  which 
with  the  vernier  reading  6, 
completes  the  recorded  num- 
ber of  revolutions. 

The  action  of  the 
instrument  is  as  follows; 


The  anchor  arm  is  fixed  to  the  diagram  and  the  tracer  point  carried 
around  the  bounding  lines  of  the  figure  to  be  measured.  The  wheel 
either  rolls  or  slides  over  the  surface;  it  rolls  when  the  direction 
of  motion  is  at  any  angle  to  the  tracer  arm  greater  than  zero  and 
slides  (without  rotation)  when  the  direction  of  motion  of  the  tracer 
is  in  line  with  the  tracer  arm.  The  rolling  of  the  wheel  is  either 
direct  (i.e.  the  numbering  on  the  recording  device  is  increasing) 
or  reverse  (  i.e.  the  numbers  decrease).   The  arrangement  of  the 
parts  of  the  instrument  is  such  that  if  the  tracer  point  is  carried 
clockwise  around  the  figure  when  the  anchor  point  is  outside  of  the 
figure,  the  numbering  is  increasing,  or  the  reading  is  direct;  if 
the  tracer  point  is  moved  counter-clockwise,  the  wheel  rolls  nega- 
tively. Therefore,  we  speak  of  the  action  of  the  wheel  as  having  a 
positive  or  negative  roll.   (Caution;  The  instrument  should  be 
used  on  a  smooth  but  not  a  glossy  surface.   Smooth  drawing  surface 
is  best.) 

Without  discussing  the  theory  of  the  planimeter  it  will  be 
sufficient  to  state  that  the  relation  of  the  parts  is  such  that  the 


Surveying-IB  Assignment  30  Page  14 

area  of  the  figure  traceu  is  equal  to  the  product  of  the  tracer  arm 
times  the  length  of  the  roll  of  the  wheel.   Or  thus  in  symbols: 

A  =  Inc. 

in  vhich  A  =  the  area  in  square  units,  1  =  length  of  the  tracer  arm 
from  hinge  to  tracer  point,  c  =  the  circumference  of  the  wheel,  and 
n  =  the  number  of  revolutions  of  the  wheel.  All  of  these  quantities 
are  aec.su red  in  thi  same  units,  i.e.  in  inches,  or  centimeters  or 
feet,  or  other  desired  units. 

Example:  The  length  of  a  tracer  arm  is  5  inches,  diameter  of 
v;heel  C.75  inches;  if  the  number  of  revolutions  is  4.516,  what  is 
the  area  of  the  figure  traced  "when  the  anchor  point  is  outside  of 
the  figure? 

A  =  5  x  0.75  x  3.14  x  4.516  =  10.54  sq.in.      (A  =  Ixd  xTTxn) 

When  the  anchor  point  is  fixed  within  the  area  to  be  measured, 
the  behavior  of  the  wheel  is  such  that  the  number  of  revolutions  re- 
corded ^.vill  £,ive,  not  the  area  of  the  figure,  but  the  area  of  the 
figure  minus  a  certain  area  knov,n  as  the  area  of  the  zero  circle  (or 
zero  circumference).  This  is  better  known  as  the  correction  area, 
since  this  area  must  be  combined  with  the  result  obtained  when  the 
anchor  point  is  within  the  oounding  line  of  the  figure  traced.  We 
shall  call  this  quantity  the  "correction  area". 
The  Constant  of  the  Planimeter 

For  any  fixed  length  of  arm  and  circumference  (diameter)  of 
v/heel  there  is  evidently  a  constant,  which  is  the  product  of  these 
two  factors  in  the  formula  A  =  Inc,  n  Deing  a  variaole  depending 


Surveying-IB  Assignment  30  Page  15 

upon  the  extent  of  Lhe  ersa  craced. 

'Without  actually  measuring  the  length  of  arm  and  the  dia- 
meter of  the  '"/heel  this  constant,  Ic,  raey  easily  toe  determined  as 
follows : 

1.  Ley  out  a  figure  cf  known  simple  dimensions,  as  a  square 
5  in.  b;,  5  in.,  or  a  circle  of  convenient  radius,  the  area  of  which 
is  easily  computed,  or  s  rectangle  of  suitaole  dimensions;  the  pur- 
pose in  any  case  being  to  have  a  figure  of  suitable  size  whose  area 
may  be  readily  and  precisely  computed. 

2.  Fix  the  anchor  point  outside  of  the  figure  and  in  such 
position  that  the  tracing  point  may  be  carried  around  the  bounding 
lines  conveniently.  After  setting  the  anchor  point  trace  the  lines 
to  see  if  this  condition  ootains. 

3.  Note  the  initial  reading,  of  the  counting  device  -when  the 
tracing  point  has  been  set  at  some  point  on  the  bounding  line.  This 
is  best  at  a  corner,  if  the  figure  is  made  up  of  straight  lines,  or 
at  a  marked  point  on  the  circumference  if  a  circle. 

4.  Carry  the  tracer  around  the  figure  clockwise  until  it  has 
passed  ever  the  entire  boundary  and  rerd  the  counting  device  for  the 
completed  record.   The  difference  between  the  initial  and  the  final 
readings  is  the  number  of  revolutions,  n,  for  this  measurement. 

5.  We  nov:  ha\e  the  area  of  the  figure,  A,  and  the  number  of 

revolutions,  n.   Substituting  these  quantities  in  the  formula  A  = 

i 

Inc,   ive  may  find  the  constant   of  the   instrument   Ic ;   for: 

Ic  =  A/n. 


Surveying-IB  Assignment  30  Page  16 

Likewise  we  may  measure  the  length  of  the  tracer  arm  (from  the 
hinge  to  the  tracer  point)  and  find  c,  or  the  diameter  of  the  wheel 
may  be  measured  directly  and  c  computed  from  £  =  IT  d. 

But  it  is  sufficient  to  determine  the  constant  Ic,  as  ex- 
plained above,  and  any  areas  measured  are  then  easily  computed  by 
multiplying  the  number  of  revolutions  (n)  in  any  case  by  the  con- 
stant to  obtain  the  area. 

In  determining  the  constant  as  above  it  is  always  best  to  make 
several  trials  and  take  the  mean  of  these  as  the  most  nearly  correct 
value. 

(227)       To  find  the  value  of  the  "correction  area"  construct  a  figure 
of  simple  dimensions,  fix  the  anchor  point  within  the  bounding  line 
and  trace  the  figure  noting  the  roll  of  the  wheel.  When  the  tracer 
is  carried  clockwise  and  the  roll  is  positive  we  get  a  positive 
value  for  ri  (i.e.  +n)  but  if  the  roll  of  the  wheel  is  negative  then 
we  have  a  negative  value  for  n.   In  the  same  way  if  the  tracer  is 
carried  counterclockwise  and  the  roll  of  the  wheel  is  positive  we 
have  -n;  if  the  roll  of  the  wheel  is  negative  we  have  +n.  Care  must  be 
taken  to  observe  these  facts. 

The  value  of  the  result  as  thus  obtained  is  Inc  =  Ak  -  Ac,  in 
-vhich  _l£  is  the  constant  (determined  as  above),  n  is  the  number  of 
revolutions  and  may  be  either  positive  or  negative,  Ak  is  the  com- 
puted area  of  the  known  figure,  and  Ac  is  the  correction  area. 

Hence  the  correction  area, 

Ac  =  Ak  -  (±nlc) 


Surveying-IB  Assignment  30  Page  17 

It  may  be  observed  that  if  the  roll  of  the  wheel  is  positive 
the  correction  area  is  smaller  than  the  area  traced;  if  the  roll  of 
the  wheel  is  negative  the  correction  area  is  greater  than  the  area 
traced;  also,  if  the  difference  between  the  initial  and  the  final 
readings  is  zero,  the  correction  area  is  equal  to  the  area  of  the 
figure  traced.  Stated  thus: 

Ac  =  Ak  -  (lc.+n)  =  Ak  -  Icn,  Ak  greater  than  Ac 
Ac  =  Ak  -  (Ic.-n)  =  Ak  +  Icn,  Ak  less  than  Ac 
Ac  =  Ak  -  (Ic.zero)  =  Ak  -  0,  Ak  =  Ac 

In  using  the  planimeter  for  finding  the  area  of  a  portion  of 
a  map  in  square  niles,  acres,  etc.,  it  is  necessary  to  take  the 
scale  of  the  map  into  consideration.   If  the  scale  is  given  so  many 
acres  to  the  square  inch,  or  so  many  square  miles  to  the  square  inch, 
then  it  is  only  necessary  to  reduce  the  number  of  square  inches  to 
acres  (or  square  miles)  by  multiplying  by  the  proper  ratio.   The  same 
would  be  true  where  the  area  is  found  by  planimeter  in  other  units 
and  the  value  of  one  unit  known  in  some  other  unit.  To  illustrate: 

Suppose  the  map  were  drawn  to  scale  of  50  miles  to  the  inch, 
then  the  square  inch  would  represent  2500  square  miles.  Again,  if 
the  scale  were  1  inch  =  400  feet,  then  1  sq.  in.  would  equal  160,000 
square  ft.,  or  —  -  acres.  Hence,  if  the  area  were  found  by  plani- 


meter  to  be  m  sq.  in.,  then  the  area  in  acres  would  be       m  acres. 

43560 

(1  acre  =  43,560  sq.  ft.) 

The  simpler  makes  of  planimeter  have  the  tracer  arm  fixed  (not 
adjustable)  hence  the  constant  Ic  of  such  having  been  determined  for 


Surveying-IB  Assignment  30  Page  18 

any  given  unit  area,  the  namber  of  revolutions  alone  constitutes 
the  only  variable  to  be  observed.  Other  makes  have  adjustable  arms 
and  are  provided  with  a  graduated  scale  or  gauge-marks  that  enable 
the  setting  of  the  instrument  to  read  directly  square  centimeters, 
sq.  meters,  sq.  inches,  acres,  etc. 

The  planimeter  is  made  in  many  styles  and  adapted  to  many 
purposes  such  as  finding  the  areas  of  cross-sections,  profile  sec- 
tions, steam  engine  indicator  diagrams,  land  surfaces,  and  in  fact 
finding  any  area  that  may  enter  into  a  general  or  specific  proolem. 

References 

Breed  &  Hosmer,  Vol.  I,  pp.  445-461 
Raymond,  See  index  and  pp.  172-179 
Johnson,  pp.  262-270,  and  pp.  143-161 
Tracy,  pp.  485  to  500 

. 

Problems  to  Assignment  30 

1.  A  quadrangular  field  has  the  following: 

Bearing  Defl.  angle 

A-3   S  30°  00'  E        459 
B-C  434 

C-D  521   117°  00'  L 

D-A  397 

Int.  Angles  :  ABC  =  115°  30';  CD*  =  109°  30' 

Construct  the  figure  by  tangents  and  chords,  scale  1  inch  =  5  ft. 
Accompany  drawing  with  complete  data. 

2.  Find  the  constant  (lc)  of  a  planimeter  which  in  tracing 
three  times  the  perimeter  of  a  square  4  in.  x  4  in.  gave:  initial 
reading  =  2.734,  a  =  4.325,  b=  5.926,  c  =  7.527. 

3.  If  the  tracer  arm  is  5  inches,  what  is  the  diameter  of  the 
wheel  of  the  planimeter  used  in  proolem  2? 

4.  The  same  planimeter  was  used  to  trace  a  portion  of  a  map 
with  scale  1  inch  =  4  miles,  initial  reading  3.472,  final  reading  5.555. 


UNIVERSITY  OF  CALIFORNIA  EXTLNS  ION  DIVISION 
Correspondence  Course 

Elements   of  Surveying 

Surveying   ID  Swaiford 

Assignment  31 

Triangulation  and  Base-Line 
Foreword  :- 

This  assignment  will  treat  of  Trian&ulation  systems 
as  used  with  Base-Lines   in  surveying,  the  methods  of  measuring  a 
base-line  and  the    location  of  triangulation  stations  and  the 
adaptation  of  the  method  to  topographic    surveying. 
(228)  Base-Line  :- 

Primarily,   any  system  of  triangulation  begins  with  a 
base-line  accurately  determined  by  the  most  precise  methods  of 
measurement  and    ite   location  also  accurately  determined  by 
astronomical   observation. 

The  region  covered  by  a  triangulation  net  is  first 
carefully  reconnoitred  to  obtain  the  most  advantageous  points 
for  purposes   of  observation.      These   are  determined   by  tneir 
prominence,    intervisidility ,   and  accessioility  for  the  purpose 
used.      The   situation  of  triangulation  points   should  be,   gener- 
ally,  o  prominent  one,    such  as  peaces  or  summits,    headlands, 
steeples,    light-houses,    etc.;   but  where  the  points  are  to  be  used 
for  observing  stations,    it  must    De  possible  to  occupy  them  with  a 
transit   or   theodolite.      Therefore  some   of  the  above  described  points 
would  have  to  be   eliminated  from     the    list  given. 


El em.  of  Surv.  IB         Assignment  51  Page  2 

Another  consideration  is  that  of  the  location  of  the 
proposed  base-line,  which  should  be  chosen  in  a  comparatively  low 
altitude  and  preferably  in  a  straight  and  nearly  level  stretch  of 
sufficient  extent  to  permit  its  being  projected  in  a  straight 
line  or  nearly  so.   If  the  region  covered  by  the  triangulation 
system  emoraces  hills,  valleys,  woods,  and  plains,  it  is  evident, 
therefore,  that  much  attention  must  be  given  to  the  work  of  re- 
connaissance ,  so  &s  to  overcome  possiole  obstructions  to  the 

proper  carrying  out  of  the  work.,. 
F 

—__  ^—   r 

(229)      Suppose  the  Base- 
line AB  in  the  adjoining 
Fig.  97,  representing 
what  is  called  a  base- 
line net,  has  been 

established  and  accurate- 
Figure  97 

ly  measured  °£  subsequently  described  in  this  assignment.   The  points 
C,  D,  E,  F,  G,  etc.  are  then  chosen  so  that  the  work  of  measuring 
the  necessary  angles  in  the  configuration  shown  may  proceed  unobstruct- 
ed.  It  is  essential  to  good  work  in  this  case  that  A,  B ;  C,  and  D 
shall  be  intervisible  each  from  all  the  others,  and  that  the  triangles 
ABC,  ABD.  .aCD,  and  BCD  shall  be  well  proportioned.  By  this  is  meant 

that  the  sides  should  be  nearly  equal.   None  of  the  angles  should 

o  o 

be  less  than  30  or  more  than  120  and  the  ^ore  nearly  they  ap- 

o 
proach  60  the  better.   The  diagonal  CD,  being  especially  for  the 


Elem.  of  Surv.  lb 


31 


Page  3 


purpose  of  checking,  need  not  make  large  anglee  with  the  other 
lines,  but  it  would  be  best  to  secure  angles  greater  than  30°  if 
possible. 

In  the  triangle  ABC  the  line  AB  (base-line)  is  known; 
hence,  to  find  the  sides  AC  and  BC,  the  angles  CAB  and  CBA  are 
carefully  measured  with  a  transit  or  theodolite,  and  the  law  of 
applied,  thus: 


AC 


Sin  C 


,  and  BC  * 


Sm  C 


So  also  in  the  triangle  ABD,  the  sides  AD  r,nd  BD  may  be  computed 
from  the  known  side  AB  (base-line)  and  the  angles  at  A  and  B. 

The  parts  AC,  BC,  AD,  and  BD  having  been  determined,  and 
the  angles  included  having  oeen  measured,  we  aay  proceed  to  compuie 
the  diagonal  CD-   This  completes  a  quadrilateral  known  as  the  base 
net,  and  since  the  subsequent  expansion  of  the  triangulation  system 
raust  depend  for  its  correctness  upon  the  accuracy  with  which  the 
parts  of  this  quadrilateral  are  determined,  it  is  essential  that 
careful  h&ed  be  taken  to  perfect  the  measurements  and  computations 
upon  which  the  determined  parts  depend. 

The  angles  of  the  quad- 
rilateral are  aeasured  either 
with  a  theodolite  or  a  transit; 
if  the  transit  is  used  the 
method  of  measuring  angles  by 
repetition  is  employed.  The 


Figure  98 


Elem.  of  Surv  IB        Assignment  31  Page  4. 

transit  is  set  up  at  A,  the  instrument  carefully  centered  over 
the  exact  end  of  the  base-line  and  the  plates  carefully  leveled. 
Too  great  care  cannot  be  taken  to  set  the  vertical  axis  vertical, 
and  to  have  the  tripod  firmly  planted  and  the  instrument  in 
perfect  adjustment-   The  accuracy  of  the  results  in  angle  measure 
will  depend  much  upon  the  handling  of  the  instrument;  especially 
ie  this  true  with  respect  to  the  clamping  of  plates  and  the  use 
of  tangent  screws;  also  attention  must  be  given  to  the  manner  of 
turning  the  transit  on  its  vertical  axis  in  sighting  and,  again, 
in  the  inverting  of  the  telescope  in  the  act  of  "plunging". 
Clamp-screws  should  be  brought  firmly  to  seat,  but  never  clamped 
very  tightly.  The  very  act  of  urging  the  screw  against  its 
bearing  may  throw  the  instrument  out  of  level  or  cause  a  slight 
rotation  of  the  whole  about  the  vertical  axis.  A  tangent  screw 
will  act  better  when  opposing  the  spring,  than  when  the  spring  fol- 
lows the  screw;  so  it  is  better  always  to  set  the  vernier  index 
before  clamping  so  that  a  clockwise  movement  of  the  tangent  screw 
will  be  required  to  bisect  the  signal  or  point  sighted  upon. 
During  the  series  of  readings  by  repetition  the  plate  of  the  tran- 
sit should  not  be  disturbed,  even  if  it  appear  that  the  vertical 
axis  is  not  truly  vertical;  if  it  is  thought  best  to  readjust  the 
verticality  of  the  instrument,  this  must  be  done  and  a  nev;  set  of 
readings  made 
(230)  Repetitions  of  angle  should  be  made  as  follows:  With 


Elem.    of  Surv.    lb  Assignn-ent  31.  Page  6. 

the  telescope  normal,    set  the  A  vernier  at  zero  and  check  by  ob- 
serving the  B  vernier.      Record   both  readings.      Unclamp  the    lower 
motion;    set   intersection  of  cross-hairs  on  left-hand    signal 
(i.e.   when  instrument   is  at  A,    sight   on  C);  bisect  precisely  by 
means  of  the   lower  tangent   screw.      (Caution:     The   signal,   at  C  for 
example,  may  present  a  phase   such  that   one   side  of  the   signal  rod, 
plumb-bob  or  other  device   shall  be  mistaken  for  the  middle   of  the 

same;   endeavor  to  eliminate   such  a  condition.)     Unclamp  upper  mo- 

and   sight  right-hand   signal  on  B;  clamp  the  upper  motion 

tioryand  perfect  the    bisection  of  signal  with  upper  tangent-screw. 

Read   and   record  full  angular   readings   of  both  A  and  B   verniers. 
Continue  the   repetitions  by  setting  on  left-hand   signal  with  low- 
er motion,   then  upon  right-hand   signal  with  upper  motion  the    . 
requisite  number  of  times  to  produce  the  number   of  repetitions  de- 
sired,  but  recording  only  the   final   readings   of  A  and  B  vernier. 

Now  (without  disturbing  either  the   setting  of  the 
instrument  or  the  vernier   index)      invert  the   telescope  and  take 
an  equal  number   of  readings   of  angle  with  telescope    "plunged". 
The  mean  of  the  two  repetitions   is   the  value   of  the  angle 
measured.     Record  this  as  the  mean  angle. 

Let   it  be  supposed  that  we  have   just  measured  angle  a 
at  A     in  Fig.    98.      Proceed   in  like  manner  to  measure   angle  h 
at  A;   then  the  total  angle  a  +  h,   and  the  exterior  angle  CAD,   thus 
closing  the  horizon  about  A.      Now  proceed  to  B   and  measure   in 
turn  angle  d,  angle   e,   d  •*•  e,   and  exterior  angle  CBD.     Next  occupy 
C,  measuring  angles,   b,   c,   b  •*•  c,    and  exterior  angle  ACB ;   finally, 


Elem.    of  Surv.    13.  Assignment  31.  Page  6. 

occupy  D,    determining  angles,   g,   f,    g+f,   and  exterior  angle  BDA. 
All  angles  are  actually  measured  and  not  computed  from  partial  OD- 
servec  data;   for  example,   at  the   last  point   occupied  aoove,    i.e. 
at  point  D,  me  a  sure   g  and  £ ,  then  measure     g  -t-  f ;  do  not   assume 
that  the  whole  angle   is  equal  to  the     sum  of  its  parts;   so  also 
the   exterior  an^le   is  measured,     not  corr.puted  from  360  -  (g  +  f ) . 

The  test   of  the  accurac;/   of  the  work  of     measurement   is   of  course 

o 
th°.t  g  +  f  e  int.    angle  ADB  ;   and  g  +  f  -t-  ext.    angle  BDA  *  360   . 

These  are   checks  used    in  the   field   and   should  be  so  applied,   a 
serious   discrepancy  being  at   once  corrected. 
(231)  Having  completed  the  angle  measurement  at  all  four 

stations  of  the  quadrilateral  AC3D,  before  making  computations  of 
the  sides  and  the  diagonal  CD,  it  is  essential  that  the  angles  of 
the  Quadrilateral  should  be  carefully  adjusted. 

I he   following  conditions   should  obtain: 

1.  Ih&   sum  of  all  the  an6les  aoout  any  station 

o 
should  equal  360     (the  field  test   should  apply;. 

2.  The  sun  of  all  the  angles  of  the   quadrilateral 

o 
should   equal  560°;    i.e.      a-irb-rc+d  +  eTf  +  g  +  h"      360   . 

3.  The   sum  of  the  angles   of  any  triangle   should   be 
180°;  e.g.      b  +  a  +  h-g*  180°,   and  c+d  +  e  +  f*  180°. 

4.  Since   angle   2   =  angle    4   (vertical  angles  at  0), 
then  c  -1-  d  =  h  +  g;     also,    since  angle    1  -   angle  3,   a  f  b  s   e  +  f. 

In  making  the   adjustments   it   is  assumed   that  the   error 
in   any  case  mny    oe   distributed   by  equal  parts   to  each  angle, 


Elem.  of  Sun/.  IB.         Assignment  31.  Page  7. 

1/3  to  each  angle  of  a  triangle,  1/4  to  each  angle  of  a  quadrilater- 
al and  1/2  to  each  pair  of  equals. 
(232)  Finally  a  test  of  the  sides  should  be  made  as  follows: 

Since  AC=  m  Sin  <b  *  c)  .  and  CB  =  AB  Si"(b  *  G).  it  follows 
Sin  d  Sin  a 

that; 

Sin  (b  +  c)      Sin  (b  +  c) 


AC    :  CB  =  AB 


sn  d          :   <  Sin  a 


Cancelling  AB   sin  (b  +  c)   and  applying  the  test   of  the  primitive 

AC  Sin  d 

proportion    —  = after  computing  AC  and  CB. 

CB  Sin  a 

A  further  equation  of  condition  for  the  quadrilateral  n. 
should  also  obtain: 

Sin  a   Sin  c    Sin  e    Sin  g 

Sin  b  x  SirTd"  X  Sin  f  x  Sin  h  =  * 

or  expressing  the  same  logarithmically; 

log  Sin  a  -t-  log  Sin  c  +  log  Sin  e  +  log  Sin  g 

-  (log.  Sin  b  +  log  Sin  d  +  log  Sin  f  4-  log  Sin  h)  =  0 

The  further  adjustment  of  the  angles  may  be  necessary 
in  order  to  bring  about  the  above  conditions. 
(233)  Measurement  of  the  Base -Line. 

The  site  of  the  Base-line  is  first  determined,  the  ex- 
treaities  are  staked  out,  and  the  measurement  of  its  length  then 
made. 

Various  methods  have  been  employed  froa  time  to  tine, 
but  that  now  followed  is  with  a  steel  tape  of  known  standard  and 
used  in  the  field  under  suitable  conditions  of  wind  and  temperature, 


Elem.  of  Surv.  liJ.        Assignment  31.  Page  8. 

generally  at  a  normal  tension  for  compensating  sag. 

In  Assignments  3  and  4,  the  discussion  of  linear  measure- 
ment was  given  fully  anc  it  -will  be  unnecessary  here  to  repeat  these 
instructions;  however ,  it  may  be  advisable  to  restate  the  several 
corrections  in  tape  measurement  as  applicable  to  the  case  in  hand. 

(a)  The  tape  should  be  corrected  for  erroneous  length. 

This  requires  that  the  tape  be  compared  with  a  standard 
and  the  error  carefully  determined.   Suppose  that  the  tape  is 
100  feet  long  (nominally)  and  the  ar.ount  that  the  tape  is  longer 
or  shorter  than  this  when  compared  with  standard  is  found.  The 
correction  to  the  measured  line  is  applied  for  every  hundred  feet 
of  length  in  the  measured  line.  Again  if  a  fractional  tape 
length  remains  -  say  37.175  feet  or  69.827  feet,  then  that  portion 
of  the  tape  used  in  making  this  fractional  measurement  should  be 
tested,  by  standard  to  determine  the  correction  for  this  special 
segment.  Usually  it  is  known  or  assumed  that  the  discrepancy 
between  the  used  tape  "nd  the  standard  is  uniformly  distributed 
throughout  the  whole  length  of  the  tape  and  the  correction  is  so 
applied. 

Hence,  to  correct  for  standard,  multiply  the  measured 
length  of  the  line  by  the  error  in  one  tape  length,  divide  by  the 
length  of  the  standard  (100  feet  in  this  case),  and  add  the  cor- 
rection if  the  tape  is  longer  than  the  standard,  or  subtract  if 
shorter  than  the  standard. 


Elera.  of  Surv.  IB.        Assignment  31.  Page  9. 


Lc  =  corrected  length  of  line,  L  =  measured  length  of 
line,  e  =  difference  between  the  standard  100  foot  tape  and  the 
nominal  one  hundred  foot  tape. 

(o)  Each  measured  segment  of  the  line  should  be  cor- 
rected for  temperature. 

The  tape  is  standard  et  62C  Fanr. ;  therefore  measure- 
ments taken  at  other  temperatures  must  be  corrected  as  follows :- 

The  temperature  T  of  the  tape  is  observed  usually  at  two 
points,  a  fe«v  feet  from  en.cn  end,  the  menn  of  the  observed  values 
being  tr.lcen  for  the  value  of  I.  The  coefficient  of  expansion  for 
the  ordinary  steel  tape  is  approximately  0.0000065  -  a  (The  cor- 
rection t  a  which  is  very  small  nay,  of  course,  be  ignored). 

This  coefficient  is  per  foot  per  decree  Fahr.  ;  hence  mul- 
tiply the  difference  in  temperature  (temperature  of  tape  minus  the 
temperature  of  standard;  by  the  length  of  line  times  the  coeffici- 
ent vhich  gives  the  correction  to  be  added  if  temperature  is  above 
standard,  to  be  subtracted  if  temperature  is  below  standard. 

Lc  =  1^  t  (xx  -  T  )  0.0000065 

In  which  1  s  correct  length  of  segment,  l,a  =r  measured 
length  of  segment,  T^  is  the  temperature  (observed  mean),  T  is  the 
standard  temperature,  <\nd  0.0000065  the  coefficient  of  linear 
expansion. 


Elem.  of  Surv.  lb .        Assignment  31.  Page  10. 

(c)  Each  measured  segment  should  oe  corrected  for  slope. 

It  is  evident  that  even  upon  a  comparatively  level 
stretch,  unless  the  end  supports  of  the  tape  can  be  brought  to  the 
sane  elevation,  the  length  of  segment,  1,  is  not  the  horizontal  dis- 
tance but  the  slope  distance  for  that  segment.   Hence,  a  reduction 
to  the  horizontal  is  required. 

This  may  be  secured  in  one  of  two  ways;  either  the  angle 
of  slope  must  be  measured ,  or  the  difference  of  elevation  of  the 
two  ends  of  the  segment  must  be  found  and  the  appropriate  correc- 
tion computed  and  applied.   The  measurement  oi'  angles  of  elope, 
except  with  special  base-line  apparatus  (notably  the  Holden 
Clinometers,  and  other  instruments)  is  troublesome;  and  even  with 
such  special  apparatus  gives  no  more  reliaole  results  than  the 
method  here  described,  as  follows: 

With  engineer's  level  or  transit  used  as  such  take  rod 
readings  at  both  ends  of  the  segnent;  preferably  set  up  instrument 
equidistant  from  the  two  ends  thus  eliminating  error  in  adjustment 
of  the  line  of  sight  perpendicular  to  the  vertical  axis.   The  dif- 
ference of  the  two  readings  so  obtained  is  the  required  difference 
in  elevation;  this  difference  may  be  easily  found  to  the  nearest 
1/100  of  a  foot  which  is  well  within  the  degree  of  accuracy  desired, 
as  a  difference  of  1/100  of  a  foot  is  about  that  of  20"  of  arc,  for 
a  distance  of  100  feet  (one  segment  of  100  feet). 

The  tape  when  compared  with  standard  is  supported 


Elem.  of  Surv.  13.        Assignment  31.  Page  11. 

throughout  its  length,  but  in  the  field  this  is  impracticable; 
therefore,  it  is  supported  only  at  the  ends  and  a  correction  for 
sag  must  be  made,  or,  what  is  more  feasible,  the  sag  may  be 
compensated  by  applying  a  tension  just  sufficient  to  accomplish 
this. 

(d)  The  correction  for  sag  is  found  from  the  formula ; 

L   f  i 

( — )  =  C  ,   in  which  C  is  subtractive  as  the  length  of  the 
24   t     s  s    

segment,  is  less  by  the  amount  of  this  correction  than  the  actual 
length.  L  is  the  nominal  length  of  the  segment  (100  ft),  1  is 
the  length  of  the  sane  (if  supported  at  the  ends,  this  is  also 
100ft) ,  w  is  the  ?reight  of  the  tape  per  linear  foot,  and  t  the  ten- 
sion applied. 

(e)  The  correction  for  tension  or  pull  is  expressed  by 

the  formula     C  =  -— ,  in  which  Cp  is  additive  since  the 

SE 
effect  of  pull  is  to  stretch  the  tape,  and  hence  the  measured  I 

length  of  the   base-line   segment  is  greater  than  the  actual  length. 
Here  L  is  the   nominal  length  of  the  tape   (100  ft),     t     is  the  pull 
or  tension,    S  is  the  cross-sectional  area  of  the  tape   in  the   same 
unit  as  L     (i.e.   the   foot)   and  E   ie  the  modulus  of  elasticity  of 
the  material  of  the  tape.      The  modulus   is  taken  as  30,000,000  Ibs.  , 
being  that  of  steel  used   in  tapes  of  this  kind. 

(f)  Nonael  tension  is  a  tension  which  applied  to  the 
tape  compensates  for  the   sa=c;   or   since  the  C     is  a  subtractive  cor- 

S 

rection  and  C  is  additive  we  may  put    Cs  =  C   and  find  the 


Elem.  of  Sur\.  IB. 


Assignment  31. 


Page  12, 


resultant  value  of  t  in  the  equation,  thus: 


—     ( — )      = ;   and  this   solved  for  t  gives     t 

24    t      SE  ' 


VsEfr2!* 
24 


This  tension  applied  to  all  measurements  removes  the 
troublesome  computations  for  sag  and  tension;  the  results  obtained 
are  equally  reliable  T?ith  other  more  complex  method. 
(234)  Broken  Base -Lines 

If  feasible  a  base-line  should  be  measured  in  a  straight 
line,  but  as  it  is  sometimes  more  important  that  the  case  should 
have  the  desired  extent  and  location  of  its  extremities  than  that 
its  measured  parts  should  oe  in  the  same  straight  line,  a  "broken 
base"  is  often  chosen  intentionally,  and  the  broken  base  is  then 
reduced  to  a  straight  base,  as  follows: 

Suppose  that  the  segments  AC  and  CB  of  a  base  have  been 


Fig  99. 
measured  and  that  these  deflect  at  C  by  the  angle 6.    Then  the 

base-line  ^B  is  computed  from  the  trigonometric  law  of  cosines,  thus 

AB     =  AC^  +  CB      -  2(AC  x  CBj   cos  ACB ;  or  choosing 

instead   the   deflection  anrlefr"    (18C     -  ACB)    and   extracting  the 
square-root   of  both  numbers 

AB   =~\/A°2  +  CB2  +  2(AC  x  CB) 


Elera.  of  Surv.  IB.       Assignment  31.  Page  13. 

From  the  aoove  an  approximate  formula  is  derived  which 
gives  satisfactory  results  when  applied  in  cases  where  the  angle 
6  does  not  exceed  from  3°  to  5°.   The  formula  is: 

2 

A3   =  AC  -f  CB   +  0.00000004231     AC  *  CB   - 

AC   x  CB 

As  logarithmic  computation  is  here  desirable  the  log- 
arithm of  0.00000004231  is  2.626424  -  10. 

If  the  angle  6  is  larger  than  5°,  then  it  would  be  neces- 
sary to  measure  the  angles  at  A  and  B  and  compute  AB  from  the  law 
of  sines- 

The  procedure  in  the  work  of  measurement  is  as  follows: 

1)  Stakes  are  set  in  line,  by  transit  set  up  over  A,  at  in- 
tervals of  a  tape  length  (100  feet).  These  stakes  should  be  of 
substantial  size  (about  2"  x  4"  -  3  feet  long)  driven  firmly  into 
the  ground  and  cut  off  square  on  top.  On  the  tops  are  fastened 
small  strips  of  zinc  (also  2"  x  4")  on  which  lines  may  be  inscrib- 
ed to  mark  tape  lengths.   In  lieu  of  these  stages  low  tripods 
may  be  used  which  carry  suitable  clock  heads  on  which  the  zinc 
plates  may  be  fastened;  two  such  tripods  are  needed,  the  rear  one 
being  advanced  to  a  forward  position  for  each  segment  of  a  tape 
length,  while  the  other  is  left  in  position  undisturbed. 

2)  The  measurement  is  to  be  made  between  tack  centered  hubs 
r.t  the  base-line  extremities  and  the  point  on  the  ground  must  be 
transferred  to  the  top  of  the  2"  x  4"  staice  or  to  the  tripod  head. 


Elem.  of  Surv.  Id.       Assignment  31.  •   Page  14. 

To  do  this  set  up  a  transit  at  A,  carefully  leveling  same  and 
centering  on  the  point  on  hub.   Turn  off  an  angle  of  90°  from  the 
base-line  and  set  a  tack  centered  hub  8  to  12  feet  distant  from  A. 
Invert  the  telescope  and  repeat  the  setting  of  the  off-set  point; 
if  the  two  points  coincide,  then  the  off-set  point  has  been 
properly  placed;  if  the  two  points  do  not  coincide,  take  the  mean 
position.  Now  set  up  the  transit  over  this  off-set  point  and 
sight  upon  the  tack-center  in  hub  A  and  transfer  this  to  the  top 
of  the  2"  x  4"  stake  or  tripod,  marking  the  point  upon  the  zinc 
plate.   It  is  necessary  to  set  the  point  with  telescope  normal  and 
also  plunged,  in  order  to  eliminate  any  lack  of  adjustment  of  the 
line  of  sight;  if  the  two  pointings  differ,  take  the  mean  position. 
3)  Having  thus  narked  upon  the  zinc  plate  the  initial  point 

t 

of  the  base-line,  stretch  the  tape  over  this  mark  and  the  zinc 
plate  next  i'n  order  by  means  of  stretcher  bars,  one  at  each  end, 
with  dynamometers  (.spring  Balances)  attached  for  determining  the 
pull.   If  a  normal  pull  is  used,  and  it  is  better  to  use  a  normal 
pull,  see  that  the  dynamometer  records  this  tension  at  the  instant 
of  comparing,  or  setting  off  the  distance.  A  line  should  be  drawn 
on  the  zinc  plate  in  the  direction  of  the  line  at  each  station 
and  a  short  line  it  ri^ht-angles  to  this  over  the  mark,  on  the  tape 
chosen  for  the  limit  of  the  measurement;  it  is  best  to  make  this 
limit  the  100  foot  mark  or  99.9,  99.8  or  some  other  definite  div- 
ision.  Of  course  for  computation,  the  100  foot  length  is  simplest. 


Elem.  of  Surv.  IB. 


Assignment  31. 


Page  15. 


4)  While  the  tape  is  still  in  the  position  used  in  measuring 
(i.e.  while  still  suspended  in  air  and  thus  free  from  the  warmer  or 
colder  earth,  place  a  thermometer  upon  the  tape  first  at  one  end 
and  then  at  the  other,  and  record  the  mean  of  the  two  readings,  as 
the  temperature  of  the  tape. 

5)  With  a  transit  or  engineers  level,  set  up  equidistant  from 
the  tivo  ends  of  the  segment,  take  rod-readings  at  both  ends,  rod 
held  on  top  of  the  stake  or  tripod.   The  difference  of  these  two 
rod  readings  will  be  the  difference  in  elevation  between  these 
points. 

Proceed  in  like  manner  with  the  second  and  each  succeed- 
ing segment,  being  careful  to  keep  the  tape  off  the  ground,  and 
flat  with  draduations  uppermost  so  they  may  easily  be  read,  and  to 
observe  temperature,  tension,  and  elevation  in  each  case. 

6)  Record  all  data  as  observed  in  a  neat  tabular  form;  the 
following  is  suggested; 


Seg. 

Meas- 
Length 

Mean 
Temp. 

Elevation 

Corrections 

Length 
Corrected 

Total 
Meas. 
Length 

.-  * 

a 

b 

diff. 

Temp. 

Slope 

1 
2 

99.9 

100.0 

78° 
83° 

7.8 
6.7 

10.7 
8.5 

2.9 
1.8 

+0.010 
+0.014 

-0.042 
-0.016 

99.868 
99.998 

*  Add  the  several  segments 

7)  The  total  measured  length  of  the  line  should  now  be  cor- 
rected for  standard,  the  length  of  tape  being  100  *  d,  and  d  is  the 
difference  oetween  the  tape  used  (nominally  100  feet)  and  100  feet 
of  standard. 


Elem.  of  Surv.  10 


Assignment  31. 


Page  16, 


The  mean  elevation  of  the  ends  of  the  base-line  above 
sea-level  should  now  be  determined  by  running  a   line   of  differential 
levels,    from  some  bench-mark. 

8)      The   reduction  to  sea- level  is  made  by  applying  the  formula; 

rj  u 

Correction  =      £_ 
R 

in  which  B  =  the  measured   length  of  the  base-line,  h  = 
the   altitude  above   sea-level  and  R  =  the  mean  radius  of  the  earth. 

In  Fig.    100  let  B  = 
the  measured  base,    h  -  the 
altitude  above   sea-level 
and  R  r  the  earth's  mean 
radius;   then 
B    :   L    ::  R  •*•  H   :  R 


.9 


B  -  L 

B 


R  +  h  -  R 
R  T  h 


B  '  L 


arcs  are  proportional  to 
their  radii. 


and  since  h  in  the 


R 


denominator  is  very 
small  compared  with  R,  it  may  be  ignored. 

In  conclusion,  it  is  best  to  take  three  or  more  measure- 
ments of  the  base-line;  as  from  A  to  B ,  from  B  to  A,  and  again  from 
A  to  B.   The  several  tape  measurements  of  each  segment  should  be 
carefully  checked,  and  the  several  points  be  properly  aliened. 
Two  dynamometers  are  better  than  one,  placing  one  at  each  stretcher ; 
if  one  is  more  delicate  than  the  other,  there  is  some  advantage  in 


Elera.  of  Surv.  IB       Assignment  31.  Page  17. 

putting  the  less  sensitive  at  the  rear  end  and  the  more  sensitive 
at  the  forward  end,  as  it  is  only  necessary  to  note  the  approximate 
pull  at  the  rear  end,  keeping  the  zero  of  the  tape  exactly  on  the 
marks. 

Six  men  can  conveniently  be  employed  in  base-line  measure- 
ments, two  to  attend  the  stretchers;  one  at  each  end  to  observe  and 
mark  the  tape  lengths;  one  to  observe  temperature;  and  the  sixth 
man  to  handle  the  transit  for  giving  line,  and  making  off-sets, 
reading  elevations,  etc.   The  man  who  reads  temperatures  should 
act  as  recorder  as  also  the  transit  man  likewise  and  they  should 
carefully  check  all  data  on  entering  same. 

Problem  to  Accompany  Assignment  31. 

The  data  for  segments  1  and  2  are  given  on  page  15  of 
this  assignment;  for  the  subsequent  segments  3  to  8  inclusive  the 
data  are  as  follows  : 


3 

99.8 

82° 

&)  6.8 

•  b)   9.3 

4 

99..  9 

80° 

7.3 

8.4 

5 

100.0 

79° 

7.6 

7.4 

6 

100.0 

78° 

7.2 

6.3 

7 

99.9 

78C 

4.8 

2.* 

8 

87.6 

76° 

5.7 

4.3 

Compute  the  measured  length  of  each  segment;  the  total 
measured  length  of  base-line.  Apply  the  correction  for  standard: 
Tape  compared  with  standard  was  99.987  ft.  long.  The  line  measured 
was  broken  base  -  first  part  from  station  A  to  4,  where  it  deflect- 
ed 2°  52',  the  second  part  station  4  to  end  of  line. 


Elem.    of  Surv.    IB.  Assignment  31.  Page   18. 

The  elevation  of  end  h.  aoove   sea-level  was   125.8  feet; 
find  the  mean  difference    in  elevation,    and  reduce   to  length  at 
sea-level. 

The  mean  value  of  the  earth's  radius  in  feet  is  taken  to 
be  20,890,600. 

Log.  R  =  7.31995 


QUIVERS  HY  OF  CALIFORNIA  EXTENSION  DIVISION 

Correspondence  Course 
Surveying   IB.  Elements   of  Surveying  Sv/afford 

Assignment  52. 
Topographic  Surveying. 

Foreword. 

/,  general  consideration  of  the  purposes  and  methods  of 
topographical  surveying  is  the  subject  matter  of  this  assignment; 
details  of  the  subject  v.-ill  be  treated  in  the  next  assignment. 
(235)  Topographical  Surveying  consists  in  the  obtaining  of 

essential  data  of  territorial  extent  and  relief  for  the  purpose 
of  depicting  on  proper  maps  the  forms  and  elevations,  descriptive 
details,  and  pictorial  representations  of  the  physical  features 
of  land  and  water  areas. 

lo  do  this  nany  conventional  devices,  signs,  and 
symbols  are  employed;  these  conventions  have  by  long  use  become 
niore  or  less  fixed  in  character,  but  it  is  often  desirable  or 
expedient  to  reproduce  the  symbols  in  the  margin  of  the  map  when 
finished!.   These  constitute  what  is  known  as  the  legend  of  the 


AS  the  methods  .employed   include   octh  territorial  extent 
and   relief  forns   it    is  necessary  to  have  resort  to  the  various 
raep.ns  for   securing   both  horizontal  and  vertical  control  of  these 
representations.     The  horizontal  control   is   secured   by  triangula- 
tion   or   by  traverse;   the  vertical   control  by   adopting  a   suitable 
datum  plane   to  which,    through  proper   bench  marks,   the   elevations 
may  be   referred. 


Elem.  of  Surv.  IB.       Assignment  32.  Page  2. 

The  purpose  and  extent  of  the  map  or  its  survey  must 
determine  the  nature  of  these  controls:  A  triangulation  system  of 
control,  for  example,  may  be  that  of  some  portion  of  a  geodetic 
or  geological  system,  or  it  may  consist  of  a  special  triangulation 
system  built  upon  a  baseline,  assumed  and  properly  located,  and 
suitable  to  the  purpose  in  hand.  A  traverse  may  be  run  enclosing 
the  territory  covered  in  the  survey,  or  if  the  region  is  of  great 
extent  several  connected  traverses  may  be  advantageously  employed. 
A  closed  traverse  is  generally  adopted,  as  this  permits  the  usual 
checks  in  closure  both  of  the  courses  and  the  elevations,  the 
latter  being  carried  forward  with  the  angles  and  distances  as  the 
traverse  survey  proceeds.  An  open  traverse  may  be  used  to  advant- 
age in  some  cases;  especially  is  this  desirable  in  surveys  for 
roads,  railroads,  or  canals,  the  usual  open  traverse  forming  the 
framework  of  the  topographical  features. 

As  over  a  large  extent  of  territory  the  principal 
features  would  appear  as  the  mountain  ranges,  the  valleye  oetween, 
and  the  river  courses  flowing  along  the  valley  ways,  so  in  the 
smaller  areas  the  ridges  and  thalwegs  and  the  stream  lines  consti- 
tute the  most  salient  forms. 

Neglecting,  then,  the  slighter  sinuosities  of  the  streams 
of  any  region,  the  rivers,  creeks,  and  brooks,  furnish  at  once  an 
outline  of  the  reliefs  of  that  locality.   The  streams  flow  in  the 
direction  of  the  valleys  and  at  the  lowest  levels,  while  the  ridges 
form  the  heights  along  water-partings  at  the  crests  of  watersheds. 


. 


Elem,    of  Surv.    Id.  Assignment  32.  Page   3. 

Hence,  whether  the  map  desired   is  of  large  or   small  extent,    it   is 
important  first  to  determine  the  water-courses  of  the  region; 
next,   principal  elevations   of  prominent  peaks  and  especially,   ele- 
vations along  the   intervening  ridges  which  call  for   location  and 
measurement.      These  may  be  considered  the   skeleton  of  the  map  up- 
on which  the  nr.ny  minor  features  and  smallest  details  may  be 
joined. 

(236)    Instruments  use^d    in  Topographical  Surveying. 

For  this   crunch  of  surveying  a   larger  assortment  of  in- 
struments  is  avails ole  and  useful  than  for  any  other  branch.     An 
enumeration  of  these  and  their  application  may  profitaoly  be  noted 
here. 

In  the  priaarj   triangulation  work  a  transit   of  refined 
qualities  or  a  direction  theodolite   is  used  for  measuring  angles. 
The  usual  base-line   tepes  with  the  necessary   accompanying  instru- 
ments,   such  es  stretchers,    dynamometers,   and  thermometers  are  em- 
ployed  on  the   linear  measurements   of  base-lines,   traverse   lines, 
etc.      Level-rods,    stadia  rods,   and  tape-rods  are  required  for  the 
various  functions  of   such  instruments.      Levels  of  the   several  vari- 
eties  -  hand-level,   dumpy,  Wye,   and  the  high  grade   level  known  as 
the   "precise",   rre  used  as  occasion  requires;  v/hile  the  transit 
with   level  on  telescope   is  often  made  to  perform  the  functions   of 
the  more    specialized  engineer's   level. 

For  measuring  differences   of  elevation  and  especially 
for  the   determination  of  the  elevation  of  chief  or  critical  points 


Elenu  of  Surv.  IB.       Assignment.  32.  Page  4. 

the  baroneter,  either  the  cistern  type  or  the  aneroid,  is  often  suit- 
ably employed.   The  aneroid  especially  is  readily  available  on  ac- 
count of  its  portability  and  convenience. 

Ihe  transit  and  stadia  and  the  stadia  in  connection  with 
the  pl°.ne-tnble  are  valuable  as  affording  a  ready  means  of  securing 
heights  -nd  distances j  and  especially  on  work  of  details  and  in 
taking  topography  of  minor  areas  these  useful  means  are  much  and 
successfully  used. 

For  reconnaissance  topographical  surveys  the  pocket  con- 
pass  and  the  clinometer  ere  useful  instruments,  and  on  account  of 
their  lightness  and  portaoility  are  especially  in  favor  for  such 
vjork.   The  Brunton  Pocket  Transit,  used  nuch  in  mine  surveying  is 
here  favorably  mentioned  as  a  comprehensive  substitute  for  compass, 
level,  and  clinometer;  it  may  be  used  as  a  hand  instrument  and  in 
the  better  types  is  supplied  with  a  "ball  and  socket"  attachment 
fitting  it  for  use  v;ith  a  Jacob-staff. 

The  odometer  or  the  more  modern  cyclometer  attached  to 
automobiles  is  in  use  where  distances  traveled  upon  roads  and  high- 
ways by  vehicle  are  desired.  Also  the  pedometer  or  a  "pace-tally" 
is  convenient  in  keeping  count  in  pacing  work,  which  is  much  used 
in  taking  topography. 

Ihe  plane-table  calls  for  special  mention,  as,  in  its 
Various  grades  from  the  most  complete  to  the  simplest  form  known  as 
the  traverse  plane-table,  it  offers  a  most  ready  and  convenient  means 
of  traversing,  intersection,  radiation,  and  resection  methods  of 


Elezn.  of  Surv.  IB         Assignment  32.  Page  5. 

mapping  directly  in  the  field;  in  solution  of  the  three-point 
problem  (an  application  of  the  method  of  resection;  the  plane-table 
has  no  superior  for  rapid  and  efficient  work.   The  description  and 
use  of  the  plane-taole  in  surveying  will  be  discussed  in  Assignments 
34  and  35. 

Thus  it  is  seen  that  use  for  a  large  range  of  instruments 
is  found  iri  topographic  surveying  in  its  various  stages;  and  an  ac- 
quaintance with  these  instruments  and  their  uses  constitutes  a  large 
part  of  the  topographers  duties. 

(237)  Transit  lines  when  measured  by  tape  are  measured  either 

by  leveling  the  tape  or,  where  the  slope-  is  sensibly  uniform,  the 
slope  angle  may  be  taken  and  the  horizontal  distance  computed  by 
use  of  the  formula 

H.  D.  =  L  •  coso( 

where  H  D.  is  the  horizontal  distance,  L  =  the  measured  line  on 
slope  and  o<^  =  the  angle  of  elevation  (or  depression).   Or  resort 
may  be  had  to  the  formula 

H.  D.  -  L  (1  -  versoO 

as  the  versed  sine  of  small  angles  is  usually  a  number  of  few  fig- 
ures and  the  slide-rule  may  be  used  to  advantage.   For  example,  a 
line  measured  on  slope  1S3.70  ft. ;  the  angle  of  slope  o^  was 
3C  52'  (the  cosine  of  which  is  0.99772,  and  hence  the  versed  sine  = 
1  -  cos  =  0.00228);   by  slide-rule  198.7  x  0.00228  =  0.44;  then  198.7- 
0.44  =  198.26 


Elem.  of  Surv.  IB.        Assignment  32.  Page  6. 

Angles  may  be  taken  by  deflection,  bearing,  or  azimuth, 
the  azimuth  method  being  generally  preferred.   Often  an  angle  may 
be  taken  easily  by  reading  an  interior  angle  when  the  adjacent 
points  on  ooth  forward  and  back  sights  are  conveniently  marked.   If 
the  azimuth  record  is  required  the  reduction  should  be  made  at 
once  and  checked  in  the  field. 
(239)  It  is  usual  to  mark  transit  points  on  map  by  a  small 

circle  about  ^.  inch  radius  enclosing  the  point,  a  triangle  indi- 
cates a  tr iangulation  station  and  a  square  is  used  to  mark  a  stadia 
station;   thus  0  transit  point,  /\  triangulation  station, 

r— I  stadia  station.   The  transit  point  may  Decome  either  a  triangu- 
lation station  or  a  stadia  station,  in  which  case  one  sign  may  be 
superimposed  upon  the  other  as  A*Aor  IQ1  . 

Other  conventional  topographic  signs  are ;  Dwelling 

. M  _,  :"•  A k 

&••  •.— ssl     •     Barn   PXJ  ;     Ruins i !    ;  Church  LL___J     ; 


House 

Fence  •       -,  Public  Road  ^—^Z/  >  Railroad  |-  |  -  1  --|  *  I  -I 

(for  small  scale);  Railroad  i~  (  -  I  =  I  =1  (large  scale);   path  or 

Trail  ,»•'*•-. .---"*  ;  etc.   Besides  these  there  are  conventions  for 

cover  of  various  sorts,  such  as  meadows  or  graesy  plains,  pine 
forests,  deciduous  forests,  sand  dunes,  rocky  formations,  culti- 
vated fields  (shewing  crops  of  corn,  small  grain,  oeans,  etc.), 
swamp  lands,  and  groves  and  orchards. 

All  these  are  usually  included  in  a  marginal  list  desig- 
nated as  "legend"  and  a  map  where  these  or  other  arbitrary  conven- 


Elem,  of  3urv.  IB.       Assignment  32.  Page  7. 

tions  are  employed  is  not  complete  without  a  legend. 

(239)  Sines  a  topographic  map  is  the  delineation  of  the  natur- 

al and  artificial  features  of  any  locality  upon  a  plane  surface  by 
means  of  the  foregoing  conventional  signs ,  it  follows  that  a  cor- 
rect representation  should  be  true  to  facts  by  a  corresponding 
faithful  use  of  proper  conventions.  Every  point  of  the  map  corres- 
ponds to  a  definite  determined  geographic  position  in  accordance 
with  some  definite  method  adopted  for  showing  the  speroid  surface 
of  the  earth  on  i  plane;  this  method  is  called  the  "projection". 
The  representation  being  in  miniature  (usually  a  very  diminutive 
scale)  ,  the  distance  between  any  two  points  on  the  map  is  a  certain 
proportional  fraction  of  the  distance  between  the  relative  points 
in  nature.   This  ratio  constitutes  the  "scale". 

The  points,  besides  being  represented  in  projection  up- 
on a  horizontal  plane,  have  their  elevations  relative  to  a  level 
surface  indicated  in  some  conventional  way;  the  usual  conventions 
are  contour  lines,  depicting  points  of  equal  elevation  at  regular 
horizontal  elevations,  or  hachures  consisting  of  hatched  lines  of 
varying  depth  of  shade  or  interval. 

The  level  surface  to  which  the  elevations  are  referred 
is  called  the  datum  plane,  and  this  with  its  system  of  determined 
elevations  or  bench  marks  constitutes  the  vertical  control  of  the 
survey.   The  representation  of  the  variations  in  the  vertical  ele- 
ment with  reference  to  the  datum  plane  is  called  the  "relief",  and 
should  fairly  represent  the  modeling  of  the  country. 


Elem.  of  Surv.  IB-        Assignment  32.  Page  8. 

Since  all  topographic  surveys  are  based  upon  a  system  of 
triangulation  or  a  carefully  prepared  traverse,  a  sufficient  number 
of  points,  whose  geographical  positions  have  been  determined  by 
either  one  or  the  other,  or  ooth  of  the  aoove  methods,  from  the 
frame  work  for  controlling  the  less  accurate  location  of  the  many 
details.  These  points  should  oe  properly  distriouted  over  the  area 
covered  in  the  survey,  and  constitute  the  horizontal  control. 

The  determination  of  these  three  elements,  the  scale, 
the  vertical  control,  and  the  horizontal  control,  is  fundamental 
and  no  survey  or  its  map  is  complete  without  it. 

f.s  before  stated,  the  purpose  of  a  topographic  survey 
is  primarily  the  securing  of  the  necessary  data  for  the  real  pur- 
pose, the  finished  map.  Hence  the  observations  made  in  the  field 
should  be  full  and  exact  enough  to  secure  this  final  purpose.   It 
is  futile  to  exceed  in  number  or  accuracy  of  data  the  requirement 
of  the  map,  but  the  collection  of  data  must  be  carried  on  in  an 
intelligent  manner,  guided  by  a  more  or  less  complete  knowledge  of 
the  related  sciences  and  arts  employed. 

(240)  First  of  all  the  topographer  must  be  a  man  of  observing 

habits,  endowed  with  an  imagination  that  will  enable  him  to  visual- 
ize the  relief  features  of  the  country  he  attempts  to  picture.  He 
must  be  skilled  in  use  of  the  pencil  and  trained  to  sketch  the  var- 
ious relief  forms  directly  in  the  field  as  well  as  to  supply  some 
lines  and  details  from  numerical  data  and  descriptive  notes,  in 


Elera.  of  Surv.  IB.        Assignment  32.  Page  9« 

addition  to  hia  field  sketches.  Moreover,  a  topographer  should 
know  from  a  study  of  physical  features  the  causes  that  have  brought 
about  the  present  outlines  of  relief  which  he  may  be  called  upon 
to  delineate.   He  should  have  a  knowledge  of  the  forces  which  have 
caused  the  vast  and  the  recent  geological  changes,  such  as  the  up- 
lifts and  subsidences,  the  volcanic  and  erosional  forces,  the  action 

of  heat  and  frost,  the  wearing  caused  by  ice  floes  and  water;  ftnd 

changes 
again  the/effected  by  erosion  or  corroding,  by  the  transporting 

power  of  streams,  and  the  action  of  tides  and  currents  on  the  pro- 
duction of  land  forms.   Not  all  persons  can  make  good  topographers; 
indeed  but  few  of  the  many  ever  qualify  for  good  work  beyond  the 
crudest  stages  of  skill  and  knowledge  -  for  this  work  is  artistic 
in  its  nature  and  hence  exacts  from  him  who  would  successfully 
follow  it,  much  patience  and  intelligent  practical  experience. 


Elem.  of  Surv. 


Assignment  32. 


Page  10. 


QUESTIONS  TO  ACCOMPANY  ASSIGNMENT  32. 

1.  After  reading  Assignment  23,  state  the  several  characteristics 
of  contours;  also  get  from  a  dictionary  the  meaning,  spelling 
and  correct  pronunciation  of  the  v;ord  "contour". 

2.  Define  scale,  horizontal  control,  vertical  control,  datum, 
thalweg. 

3.  What,  in  your  estimation,  are  the  essential  qualifications  of 
a  good  topographer?  What  are  some  other  desirable  qualifica- 
tions? 


References : 

Breed  &  Hosmer 
Johnson 
Raymond 
Tracy 


Vol.  I.   pp.  30G  -  320. 
Chap.  VIII. 
Chap.  IX. 
Chap.  XXVII. 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 


Surveying-IB 


Mr.  Svrafford 


Corrsspondence  Courses 
Elements  of  Surveying 

Assignment  33 
Solution  of  Problems 

Computations  and  Results 

To  be  returned  to  student  after  submitting  Assignment  33. 

The  actual  computations  of  H.D.  and  V.H.  for  course  A  -  B  are 
here  given.  In  all  other  courses  and  for  Side  Shots  the  results 
only  are  shown. 


Course 

H.D. 

,y.a. 

Elevations  (Adj) 

A—  B 

385.3 

+47.76 
(47.79) 

B  247.73 

B—  C 

395.9 

-26.11 
(26.07) 

C   221.72 

C--D 

487.6 

+38.56 
(38.69) 

D  260.41 

D~  2 

630.3 

-56.  9S 
(56.95) 

E   203.46 

E--A 

598.4 

-   3.4-5 
(3.46) 

A  200.00 

+86.42 

-86.55 

Diff 

-  0.13 

Computations 

log  £  (98.5)  =  1.99344 
"  S  (3.96)  =  0.59770 
"  cos  OC(7°4')  =  9,99669 
n  n  n  (704!)  =  9.99539 

384.2  =  2.58452 
1.1 

385.3  =  H.D.  A—  B 


log  1  (98.5)  =  1.99344 
"  S  (3.96)  =  0.59770 
"  cos  oC(7°41)  =  9.99669 

"   sin  <X(7°4')  »  9.08999 

47.62        =  1.67782 

0.14 

47.76  Elev.  of  B  above  A 
200.00 

247.76  Elev.  of  B  above 
Datum. 


Surveying-IB.   Solution  of  Problems,  Assignment  33,  page  2. 


Computation  o_f  Coordinates  f_or_  Plotting 


Course 

Bearing 

Dist 

Conp 

.Lil  C  • 

uted 

Dep. 

Bala 
Lat. 

need 
Dep. 

Coordi 

y's 

nates 
X's 

A--B 

N40010'E 

385.3  ft 

+294.4 

+248.5 

+294.4 

+284.3 

A  581.6 

A  120.0 

B—  C 

N  87'00'r 

498.1  ft 

+  23.7 

+497.4 

+  26.7 

+497.0 

B  875.0 

B  368.3 

C--D 

S  25°02'E 

487.5  ft 

-441.8 

+205.3 

-441.8 

+206.2 

C  902.7 

C  865.3 

D—  E 

S  50°30'W 

S30.3  ft 

-400.9 

-486.4 

"-400.9 

-486.8 

D  4C0.9 

D1071.5 

E--A 

N  41a40'W 

698.4  ft 

+521.7 

-464.3 

+521.5 

-464.7 

E  60.0 

E  584,7 

Lat  Diff  =0.1 

Den  Diff  *  1.5 


For  Plotting  assume  origin  of  Coordinates 
at  the  lower  left-hand  corner  of  border 
on  Map.   120  ft.  to  left  of  A,  50  ft 
below  E. 


Computations  _of  Latitudes  and  Departures 


A-B 

B-C 

C-D 

D-E 

E-A 

Lat. 

294.4 

26.7 

441.8 

400.9 

521.7 

log.  Lat. 

2.46899 

1.41612 

2.64522 

2.60306 

2.71744 

n   Cos. 

9.88319 

3.71880 

9.95716 

9.80351 

9.87334 

"   Dist. 

2.58580 

2.69732 

2.68806 

2.79955 

2.84410 

n   Sin 

9.80957 

9.99940 

9.62649 

9.88741 

9.82269 

n   Dep. 

2.39537 

2.69672 

2.31455 

2.68696 

2.66679 

Dep. 

248.5 

497.4 

205.3 

486.4 

464.3 

A-B 

B-C 

C-D 

D-E 

E-A 

Surve3ring-lB.      Solution  of  Problems,  Assignment  33,   page   3. 


H.D.,  Y.H.,  and  Elevation  above  Datum  of  Side  Shots 


Transit  at  A 

H.D. 

V.H. 

Elev. 

Elev.  of  A  *  200.0 

1 

383 

-16.7 

183.3 

2 

480 

-12.5 

187.5 

3 

-426 

-  4.8 

195.2 

4 

270 

+  3.5 

203.5 

5 

203 

0.0 

200.0 

6 

164 

-  4.8 

195.2 

Transit  at  B 

Elev.  of  B  »  247.8 

7 

217 

-42.3 

205.5 

8 

242 

-47.0 

200.2 

9 

377 

-54.0 

193.8 

Transit  at  C 

Elev.  of  C  -  221.7 

10 

211 

-11.1 

210.6 

11 

250 

-19.7 

202.0 

12 

232 

-24.0 

197.7 

Transit  at  D 

Elev.  of  D  =  250.4 

13 

426 

-70.6 

189.8 

14 

295 

-66.  0 

194.4 

15 

275 

-65.1 

194.3 

1C 

176 

-58.5 

201.9 

17 

209 

-56.2 

204.2 

18 

202 

-50.3 

210.1 

Transit  at  E 

Elev.  of  E  =  203.5 

19 

265 

-  4.6 

198.9 

20 

399 

+  9.8 

213.3 

DNIVEKSEY  OF  CALIFORNIA  EXTENSION  DIVISION 

Correspondence  Courses 
Surveying  iB  Assignment  34.  Mr.    SwafforcL 

The  Plane-table  and    Its  Uses 

\ 

Foreword  : 

Several  references  have  teen  made  to  the  plane-table  in  the 
preceding  assignments,   and  in  Assignment   14,   page    11  ,     the  adjust- 
merits  of  the  plane-table  were  considered;     in  the  present  assign- 
ment tre  shall  deal  with  the  plane-table  and  its  uses  someT/hat  in 
detail. 
(242  )  Adaptability  of  the  Plane-table. 

The  plane-table  is  adapted  to  many  uses  in  surveying  and  is 
especially  convenient  in  farm  or  landscape   surveys,   in  topographi- 
cal work,  and  preliminary  or  reconnaissance  sketches,      in  filling 
in  details  in  triangulation  surveys  and  sketching  for  relief  forms 
it  is  particularly  useful;     the  Y/ork  of  the  military  topographer 
is  usually  confined  to  brief,  rapid  plane-table   sketching. 

The  plane-table  consists  of  a  draughting  board  varying  in 
size  from     12"  x  15"     to     27"     x     36"     or   larger,  altho  the   larger 
sizes  are  more  or  less  unvieldy  and  hence  are  not  much  in  favor. 
A  size  about  22"  x  28"     and  made   of  light,  but  stiff  material  is 
most  convenient. 

The  board  is  mounted  upon  a  tripod  by  means   of  foot  screws, 
after  the  manner  of  the  transit,   or  by  a  modified  ball  and  socket 
arrangement  popularly  known  as  the  Johnson  head,  from  its  inventor. 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 

CORRESPONDENCE  COURSES  IN  ENGINEERING  SUBJECTS 

PLANE  SURVEYING 

COURSE  X-lB 


PLATE  X 
PLANE  TABLE  ALIDADE 

Fitted  with  11-inch  telescope;  magnifying  power,  24  diameters.  Revolving  telescope  (180  degrees)  to  check 
cross  hairs;  edge  graduation  on  60-degree  arc  graduated  on  solid  silver.  Blade  beveled  one  side,  18  inches  long, 
3  inches  wide,  with  two  bubbles  set  at  right  angles;  detachable  striding  level  to  telescope,  clamp  and  tangent  to 
vertical  movement;  fixed  stadia  hairs  set  1:100;  prism  to  eye-piece. 


Surveying  1  B.  Assignment  34.  Page  2* 

By  either  of  these  tripod  connections  the  table   (i.e.     the  board) 
may  be  brought  into  a  horizontal  position  and  also  while  remaining 
horizontal  it  may  be  turned  in  azimuth  about  its  vertical  axis. 
This  corresponds  exactly  to  the  lower  plate  and  its  motion  in  the 
transit. 
(243)  The  Alidade.        (See   Illustration,   Plate  X.) 

The  other  part  of  the  plane-table  is  the  telescope  set  up- 
on a  standard  that  has  for  its  base  a  broad  substantial  ruler  made 
of  metal  and  having  its  straight-edge       parallel  with  the  line  of 
sight  of  the  telescope;     the  telescope  may  be  turned  through  an 
angle  ranging  between  40°  and  60°  in  altitude  and  carries  a  verti- 
cal arc  for  measuring  angles  of  elevation  or  depression.     The 
ruler  and  the  attached  telescope  and  vertical  arc  constitute  the 
alidade.      It  corresponds  exactly  with  the  upper-plate  and  motion     . 
of  the  transit  (the  alidade-plate).     The  alidade-plate  of  the 
transit  has  a  graduated  limb  and  verniers,  which  are  wanting  in  the 
plane-table  alidade,   the  angles  in  case   of  the  latter  instrument, 
instead  of  being  measured,  are  directly  graphed  upon  the  plane- 
table  sheet  or  map.     For  this  purpose  a  sheet  of  suitable  paper  is 
fastened  by  means  of  clamps   or  thumb  tacks  to  the  drafting  board. 
The  plate-bubbles  of  the  transit  have  their  counterpart  in 
two  tubes  fastened  to  the  ruler  at  right -angles  to  each  other;   or, 
in  some   instruments,  a  separate   level  upon  a  movable  plate   is 
supplied,  by  trhich  the  drafting  board  may  be  made  horizontal  and 
the  vertical  axis  of  the  plane-table  may  be  brought  into  verticality. 


• 


Survey lag  It.  Assignment  34.  Page  3. 

The  telescope  also  has  a  "bubble  tube  attached  after  the  manner  of 
the  transit.   In  some  instruments  this  bubble  tube  is  detachable, 
as  it  is  used  only  for  determining  the  index  error  of  the  vertical 
arc,  after  trhich  the  arc  itself  is  used. 

Upon  the  ruler,  or  fastened!  to  the  drafting  board,  or  apart 
from  thsse,  is  a  compass  needle  for  determining  the  magnetic  mer- 
idian and  for  orienting  the  board  thereby.  As  a  full  circle  or 
even  a  large  arc  is  not  essential  for  this  purpose,  a  fragmentary 
arc  of  perhaps  5°  or  10°  either  side  of  a  mid-position  marked  zero 
(0)  suffices;  such  a  compass  contrivance  is  called  a  declinator^ 
The  detached  form  of  the  declinator  is  preferable  to  a  compass 
needle  connected  with,  the  board  or  the  ruler  of  the  alidade  as  it 
can  in  its  detached  form  be  moved  to  any  part  of  the  map  and  read- 
ily brought  into  parallelism  Trith  any  lines  of  the  sketch.  Therefore, 
it  is  made  in  a  shape  adaptable  for  this  use;  the  needle,  4U  to 
6"  in  length,  is  suspended  on  a  pivot  in  a  narrow  bronze  box.. 
6"  x  1"  in  size,  with  parallel  sides  and  a  glass  cover  to  protect 
the  needle.  The  needle  may  be  lifted  from  the  pivot  when  not  in 
use  to  prevent  wear  on  the  pivot  point. 

It  must  be  understood  that  the  plane-table  in  its  best  form 
is  not  an  instrument  of  precision;  but,  applied  with  care  and  with 
attention  to  the  several  means  of  approximate  measurement ,  it  will 
give  results  '.Tell  within  the  limits  of  accuracy  applicable  in  map- 
ping.  The  attention  of  the  student  is  particularly  called  to  the 
following  directions  in  setting  up  and  using  the  plane-table,  in 
order  that  the  best  results  nay  "be  secured  in  the  work. 


Surveying  IB.  Assignment  34.  Page  4. 

(244)       Observe  that  the  tripod  shall  always  "be  set  firmly  with  its 
feet  well  driven  into  the  ground  and  the  legs  should  not  "be  spread 
too  far  apart  nor  the  board  raised  too  high,  as  in  either  of  these 
positions  the  table  will  "be  unstable  for  working  or  too  high  or  too 
low  for  convenience  in  sighting  and  drawing  lines. 

Next  in  importance  is  the  leveling  of  the  board.  This  is 
done  by  means  of  the  bubble  tubes  upon  the  alidade  ruler  or  by  means 
of  the  detached  level  as  the  case  may  be.  The  board  is  turned  in 
azimuth  in  the  leveling  process  in  order  to  set  the  vertical  axis 
truly  vertical,  the  plane  of  the  board  being  set  perpendicular  to 
this  axis. 

The  edges  of  the  ruler  are  made  parallel  to  the  vertical 
plane  through  the  line  of  sight  of  the  telescope,  and  in  the  better 
forms  of  alidade  one  edge  of  the  ruler  is  placed  directly  in  this 
vertical  plane  through  the  line  of  sight.   Ordinarily  it  is  suffic* 
ient  that  the  lines  of  the  drawing  all  be  parallel  to  the  line  of 
direction  of  the  lines  of  sight,  but  in  soae  cases  it  is  desirable 
to  talce  sights  for  e:ctreme  accuracy,  that  are  coincident  with  the 
vertical  plane.   The  edge  of  the  ruler  that  determines  the  line 
to  be  dravm  should  be  set  upon  the  point  through  which  the  line  is 
drawn  so  that  the  pencil  point  in  drawing  the  line  passes  through 
this  point;  as  with  any  straight-edge  it  must  be  set  off  the 
point  the  thickness  of  the  pencil  pointo   In  drawing  lines,  hold 
the  pencil  against  the  ruler's  edge  always  at  the  same  angle,  other- 
wise the  line  drawn  will  be  a  curve  instead  of  a  straight  line. 


. 


Surveying  1  B-  Assignment  34.  Page  5. 

Place  the  alidade  on  the  "board  in  such  position  that  the 
e^  nay  "be  brought  to  the  eye  -piece  of  the  telescope  in  sighting; 
or  set  the  telescope  objective  end  near  enough  to  the  farther 
edge  of  the  "board  so  that  the  point  sighted  nay  "be  seen  i?hen 
sighting  an  angle   of  depression. 

Alnays  "be  careful  in  sighting  and  shifting  the  alidade; 
and   in  draining     lines  do  not  disturb  the  position  of  the  "board. 
It  is  easy  to  thror;  the  "board  out  of  level  and  a  slight  tirist  may 
turn  it  upon  the  vertical  axis. 

There  are   several  vays  of  rjaking  a  survey  -tilth  plane -table 
anc  vre   shall  notr  proceed  to  give  each  of  these   in  detail. 
(245  )  Traversing  Tri-th  Plane -table. 

This  nethocL    soaetines  called     progression,   is  sinilar  to 
traversing  vith  compass  or  transit.     The  plane-table  is     moved 
from  point  to  point  of  the  field  and  set  up  over  each  in  some 
determined  order:     the  lines  are  drarm  by  the  ruler  after  it  has 
been  centered  upon  the  point  occupied  and  the  telescope  has  been 
sighted  upon     the  adjacent  points  of  the  field,   -  on  the  back 
point  for  a  back-sight,   on    the  forv.'ard  point  for  a  fore-sight. 
The  distances  are  measured  either  by  tape  or  stadia  and  laid  off 
on  the  lines  draun,  according  to  sone  determined  scale;     thus 
the  angles  and  distances  in  each  course  are  laid  out  directly  in 
the  field  and  the  nap  may  be  embellished  by  any  additional  line 
or  data  required,    -  as,  tie- lines  to  other  points,   details  of 
j  building,   fences,     streams,   etc.       These  details  are 


Surveying  1  B 


Assignment  34. 


Page  6, 


usually  located  "by  either  one  or  the  other  of  the  methods  which 
follow:     i.e.,  by  radiation,   intersection,   or  resection.      (See 
Figure  lOlto  further  illustrate  this  plane-table  method.) 

ILLUSTRATION  OF  A  TRAVERSE   IN  DETAIL 


Fig.  101 


Traversing.   Draw  ad   representing  AD  to  scale,   set  up  table 
at  A  centering  ^   over   A;  with  alidade  on  ad   sight   D 


Surveying  1  B . 


Assignment  34, 


Page  7< 


by  turning  the  table  in  azimuth;  with  alidade  centered  on    a 
sight    B       without  moving  the  table  but  by  adjusting  the  alidade; 
scale  of     ab     equal  to    AB.      Occupy    B;     back-sight  on    A,   turn- 
ing the  table;  fore-sight  on    C;     scale       be;     also  sight    D     and 
scale       bjL       Move  to     C;     back-sight  on    B;     fore-sight  on    D, 
drawing     ccL      Occupy     D;     back-sight  on     C     and  check  through  ab 

(246)  Surveying  by  ^intersection. 

In  this  method   one  line  of  a  traverse  or  field  is  carefully 
determined  in  length  and  its  direction  selected  upon  the  sheet; 
it  is  then  drawn  to  scale;     the  plane-table   is  then  set  up  over 
one   of  the  points,   the  alidade  centered  upon  this  point,  the 
ruler  in  line  with  the  line  of  the  map,  and  the  other  point  is  now 
bisected  by  turning  the  table  in  azimuth  to  effect  this.     Figure 
which  follows  will  further  elucidate  this  method. 

ILLUSTRATION  OF  METHOD  BY  INTERSECTION 


\ 


Fig.  102 


n 


Surveying  IB.         Assignment  34.  Page  8. 

Intersection.  Draw  rag  to  scale  for  MP  in  the  field. 
Set  up  table  at  M,  centering  m  over  M.  Place  alidade  on 
mp   and  sight  P  by  turning  the  board  in  azimuth.  Center 
alidade  on  m   and  draw  indefinite  lines  toward  N  and  0  (or 
to  any  other  points  required).  Move  table  to  P;   back-sight  on 
M  by  turning  the  board.  This  orients  the  map.   Intersect  on  N, 
0  or  other  points,  thus  locating  by  intersection. 

(247)  Orientation. 

This  operation  brings  the  table  into  such  position  that 
a  given  line  or  lines  of  the  map  are  brought  into  parallelism 
with  the  same  lines  in  the  field;  in  the  two  methods  above  de- 
scribed the  orientation  was  secured  by  backsight ing  in  the 
manner  shown.  Orientation  is  sometimes  also  secured  by  drawing 
a  meridian  upon  the  map.  Then  the  map  is  turned  through  the 
necessary  angle  to  insure  its  correct  position  with  respect  to 
this  meridian;  for  this  purpose  the  compass  or  declinator  is 
useful,  and  of  course,  the  magnetic  meridian  is  most  convenient. 
In  most  plane-table  problems  the  matter  of  orientation  by  any 
of  the  means  applicable  to  the  several  oases  is  an  important  pre- 
cedent to  its  correct  and  final  solution. 


'.   :  •:      •: 


.    .  -    .    .     - 


Surveying  1 


Assignment  34. 


Page  8  A. 


)  Resection: 

A  third  method  of  surveying  by  plane-table  is  that  of 
resection.     Thia  is  especially  applicable  when  one  or  more 
points  of  a  traverse  are  inaccessible  or  when,   for  any  reason, 
it  is  desired  to  avoid  occupying  such  a  point.     In  the  Figure  103 
suppose,  for  example,     that  a  traverse     j&DCD     is  to  be  sur- 
veyed and  the 

Fig.  105 


Surveying     IB-  Assignment  34.  Page  9* 

point    B     is  situated  as  shown,   on  the  opposite  shore  of  a  stream 
or  "body  of  water.     Here  if  the  side    AB     of  the  traverse  is  known 
in  direction  and  distance,  we  may  graph  this  to  scale  upon  the 
map;  then  set  up  the  table  at  A,   centering    a     over    A;     orient 
by  placing  alidade  on     ab     and  bisect    B,     turning  the  board; 
then  keeping  the  alidade  centered  on    a     draw     indefinite     lines 
to     C     and  also     to    D     (or  to  other  points  as  desired);     next 
determine  the  distance     ac,    scaling  this  on  the  nap;     move     the 
table  to     c,     setting  the  point     c     over  the  point     C     on  the 
ground,  as  nearly  as  possible,    orienting  the  table  by  back- sight- 
ing upon    A     through    ca;     now,  with  the  alidade   sighted  on    B, 
draw      be,     or  resect  from    B     on    C-      The  triangle     bac     on  the 
map  is  proportional     (i.e.      similar  and  to  scale)     to  the  triangle 
on  the  ground        BAG,     for  the   line     ab         is  to  scale,   the  angle 
bar     is  constructed  equal  to  its  corresponding  angle     in  the  field, 
and   angle       act        is  equal  to  angle       ACB ;     hence   one  side  and 
the  three  angles  of  one  triangle  are  proportional  and  equal  respec- 
tively to  those   of  the   other.     We     may  now  intersect  upon    D, 
drawing     cd     and   similarly  for  any  other  points  desired. 

The  resection  method   is  specially  applicable   in  the  graphic 
solutions  of  the  three-point  problem  and  of  the  two-point  problem 
which  will  be  treated   in  the  following  assignment. 

(249)  Radiation. 

A  fourth  method  of  surveying  with  plane-table   is  that  of 


Surveying  1  B .         Assignment  34.  Page  10. 

radiation;  it  is  synonymous  with  the  method  in  compass  or  transit 
survey  known  as  "the  method  by  single  set-up",  which  has  already 
been  explained  in  Assignment  15,  on  Land  Surveying.  By  this 
method  a  point  on  the  map  is  centered  over  a  point  in  the  field 
whose  position  is  known  and  sights  are  taken  to  the  various  points 
whose  distance  and  bearing  (or  azimuth)  are  required.  The  distance 
is  measured  by  tape  or,  as  is  more  common,  by  stadia.  The  line  is 
drawn  directly  upon  the  map  in  the  field;  the  angles  are  not 
themselves  required  as  the  mapping  is  complete  without  the  numeri- 
cal measure  of  angles,  and  the  map  is  the  chief  consideration 
in  most  plane-table  work.  Since  the  mapping  is  done  to  scale  the 
interior  angles,  bearings,  or  azimuths  may  feadily  be  taken  off 
by  protractor,  the  lengths  of  the  sides  of  the  composing  triangles 
can  be  used  for  computing  areas  where  required  or  the  planimeter 
may  be  used  for  the  last  named  purpose. 

We  append  a  small  Military  Sketch  which  will  serve  to 
illustrate  the  application  of  the  plane-table  to  this  kind  of 
work.  The  sketch,  very  crude  of  course,  shows  how  roads,  streams, 
watershed,  fence  lines,  bridges,  etc.  are  sketched.  The  accur- 
acy of  such  work  depends  upon  the  use  to  which  the  survey  is  to 
be  put:  in  railroad  or  other  construction  work  the  measurements 
are  carried  to  a  higher  degree  of  accuracy  and  oany  notes 
accompany  the  mapped  survey. 

All  in  all  surveying  by  plane-table  is  useful  because  it 
is  sufficiently  accurate  for  the  purpose  required;  it  is  cheaper 


- 


:  .. 


•   "  ' 


Surveying  1  B-         Assignment  34.  Page  11. 

and,  when  records  or  refined  work  are  not  the  object ,  it  serves 
its  purpose  adequately;  -  many  surveys  are  made  for  a  certain 
definite  object  which,  when  accomplished,  renders  the  more 
elaborate  survey  useless  or  obsolete. 


Military        SMch 
5  want  on       V      Vic  in  i 


t 


•Sea If  :     is  ir.  =  tr^ile. 
Co  a  tour    interval  --    20  feet. 


y 


To  Vexadrro 
20  mi. 


LEGE  A/D 

Ocean  Shore  R.R. 
Standard  frirayi 
condition 

Gravel  Road   -  He, 

tr 

W^fer  obtainable  in  creek 
and  tank  eft   Swan~ton 

Creeks     crossed  ..by  wooden 
;    and    concrete  cube* 


"traffi 


c 


Creeks,    fcrdcibk 

Fifty   cords  wood  obtainable 

.  eft  fni  I  ro<jj  "terminal 
foray  plentiful 

1.  Cem«*i7  culvert 

2.  Oil   Tanks 

3.  Water  Tan  ks 

6.  Trciqhi  fcpof 

7.  Steel  Bridge 

8.  Small    Vegeifib/e    Garden 
3.    Bam  suitable   for 


Surveying     1  B .  Assignment  34.  Page  12. 

QUESTIONS  CF  ASSIGNMENT  34. 

1.  Compare  part  by  part  a  plane-table  with  a  transit. 

(Hake  replies  brief), 

2.  Give  the  steps  necessary  in  a  plane-table  survey  of  a  four 

sided  field,  using  traversing  and  radiation. 

3.  By  means  of  data  of  your  own  choosing ,  show  the  relation  be- 

tween angle  measurement  x>f  1  minute  of  accuracy  and 
lines  to  1/100  ft.  in  accuracy  and  measurement  secured  in 
mapping  to  a  scale  of  1  inch  equal  twenty  feet. 

References ; 

Breed  &  Hosraer,  Vol  II.  pp.  191-203 » 
Johnson,  pp  117-  123 
Raymond,  pp  268  -  275 
Tracy,  pp  318  -  325 


UNIVERSITY  OF  CALIFORNIA.  EXTENSION  DIVISION 

Correspondence  Courses 

Survey inr   IB  Assignment  35,  Mr.    Stafford 

PLA.NE-TABIE     -  THREE   -  POINT  PROBLEM,  Etc.. 


Foreword. 


This  Assignment  trill  deal  with  the  further  use  of  the 


plane-table,  with  a  special  application  in  the  solution  of  the 
Three-point  Problem  and  the  Two-point  Problem.. 
(250)   The  Three-point  Problem: 

A  clear  statement  of  the  problem  is  a§  follows; 

Given:-  the  location  in  the  field  of  three  points  and 
their  plotted  positions  on  the  map  and  the  station  in  the  field  of 
the  observer, 

Required;-  to  plot  this  position  of  the  observer  upon  the 
map.   (The  three  given  points  may  or  nay  not  be  inaccessible )- 

Suppose  that  we  have  the  three  given  points  in  the  field, 

B 


Fig.  104 


Surveying  IB. 


Assignment  35. 


Page  2, 


A,     a  light-house;     B,  a  church  spire;     C,  a  head-land;     and  D.- 
•which  may  ba  assumed  as  the   location  of  an  observer,  as  a  boat  at 
pea,    or  any  location  from  which  all  points  A,  B,  and  C  are  visible 
but   inaccessible.        In  the  problen  the  distances  AB<  B  C,  AC 
are  knoiTn;     it  is  required  tc  find  the  distances    A  D.,  B  D,  and 
CD.      To  do  this   it  ".rill  be  necessary  to  have  the  angles  A  D  B 
and  B  D  C;  these  nf.y  be  had  by  taking  the  bearings  of  the  several 
lines  from  D,    or  their  aziauths,    or  by  sinply  neasur:'.ng  the 
interior  angles  by  one   of  several  methods.       Aboard  a  boat  at 
sea  the  angles  nay  be  tal-cen  by  se::ta;it  -  usually  two  simultaneous 
observations  being  made,    if  this   is  possible.      Or,    on  land  a 
transit   or  even  a  corapass  may  be  -used   and  the  requisite  angles  or 
bearings  be  taken. 


Fig*   105 


Surveying  IB  Assignment  35.  page  3. 

If  the  angle  EGA  be  constructed  equal  to  angle  d  (=  EDA) 
and  angle  EAC  'be  constructed  equal  to  d!    (=EDC),  the   lines  AE 
and  CE  will  intersect  at  some  point  E  which  is  on  a  diagonal  of 
an  inscribed  quadrilateral    AECD..     AC  being  also  a  diagonal  of 
the   sane  quadrilateral;  for  EGA  =  ADE    (both  measured  by  the  same 
arc     AE),     and  ACS  =  d1,    (both  measured  by  the  arc  EC).      It  is 
now  possible  to  locate  D  since   it  is  upon  the  circle  through 
£EC     and  also  on  the  prolongation  of  EB,      i-e.     at  D,  which  is 
the   intersection  of  the  diagonal  with  the  circumference.     Hence 
the  problem  is  graphically  solved. 

The  problem  nay  also  be  solved  trigonometrically,  but  the 
plane-table  method  is  essentially  a  graphic  method  and  the  con- 
struction given  above  is  necessary  only  for  the  purpose  of  ex- 
plaining the  principles  of  the  plane-table     method. 

(251)   Methods  o£  Solution  o£  Three-point  Problem; 

There  are   several  methods   of  plane-table   solution  of  the 
three-point  problem  of  which  we  shall  explain  four:       1.     The 
Protractor  method,       2.  Bessel's    method,       3.     Triangle  of  Error 
method,     4.      Llano's  method. 

1.  Protractor  Method : 

Set  up  the  plane-table  at  the  observer's  station,  and 
center  a  three-arm  protractor   on  the  point  d   (the  point  upon  the 
table  directly  over  the  observer's  station,  D).     Direct  the  arms 
of  the  protractor  to  A,  B,  and  C     respectively,   setting  off  the 


Surveying  13-  Assignment  35.  Page  4. 

angles  ABB,  EDO-  The  points  a,  b,  c,  are  then  plotted  up- 
on the  map  in  the  relative  positions  of  A,  B,  C  in  the  field  with 
distances  according  to  the  scale  6f  the  map.  Orient  the  board 
approximately  by  estimation.  Place  the  protractor  so  that  the 
three  arms  shall  pass  through  the  points  a.,  b_,  £   in  their  re- 
spective positions,  sighting  through  a  on  A;  check  by  sighting 
through  "b  on  3   and  also  through  c  on  C.   To  do  this  may  re- 
quire a  slight  adjusting  of  the  board,  for  the  approximate 
orientation  only  partially  accomplished  the  desired  position; 
when  the  three  arras  pass  through  the  three  points  a,  b,  and  c 
and  sight    A,  B,  C,  the  protractor  center  must  be  at  d,   the 
plotted  position  of  D. 

This  is  known  as  the  mechanical  method  of  solving  three- 
point  problem.   Instead  of  a  three-ana  protractor,  a  piece  of 
tracing  paper  or  tracing  linen  may  be  used.  Draw  lines  upon  the 
tracing  paper  by  means  of  the  alidade  by  first  assuming  a  point 
on  ths  tracing  paper  and  then  intersecting  upon  A,  B,  C;  then 
secure  the  proper  orientation  by  placing  the  tracing  so  that  the 
points  aA,  bB,  cC  are  in  line.  A  point  may  now  be  pricked  upon 
the  map  through  the  assumed  point  on  the  tracing.  For  rapid 
approximate  work,  this  is  a  useful  method,  but  should  not  be  re- 
lied upon  for  great  accuracy. 
2.  Bessel's  Method. 

This  method  consists  of  constructing  the  angle  formed  by 
the  lines  from  D  (the  position  of  the  observer)  to  A,  B  ,  and  C, 
drawing  these  directly  in  the  required  position  upon  the  nap  and 


• '•" :     -•'•-'•    ••-.    •    '•  ••"•  '-.' 


.:  .      .          ".,,     "  ...'       ..'...         ••:...-•          ....... 

.....•.-        .-      -'i    t   .,      .  .-.  .  . 


Surveying  IB, 


Assignment,  35, 


page  5. 


thus  determining  the  fourth  vertex  of  the  quadrilateral.  A  study 
of  the  following  f5,gures  will  make  this  clear;  the  three  figures 
L,  11,  U,  represent  the  plane -tab la  in  the  three  steps  of  the 
solution. 


B 

N 


A  V 


A 


B 


A  \ 


4  — 

*. 


H. 


Fig.  106 


Surveying  13  Assignment  35.  Page  6. 

Set  up  the  plane-table  at  D;  place  the  alidade  upon  ca 
and  sight  A  through  a  "by  turning  the  table;  clainp  the  board  and 
with  alidade  centered  on  C,  sight  B  and  draw  the  line  from  c 
toward  B  of  indefinite  length;  this  step  is  shown  in  Figure  106 
at  L.  Again  place  the  alidade  upon  ac   and  sight  C  by  turn- 
ing the  table;  clanp  the  board  and  with  alidade  centered  on  a, 
sight  B  and  draw  the  line  fron   a  toward  B  to  intersect  the 
previous  line  so  drawn  at  e  in  the  figure;  this  step  is  shown 
in  Figure  106  at  £L  Now  draw  a  line  through  b  and  e,  place 
alidade  on  this  line  and  sight  B;  this  orients  the  nap-  Re- 
sect fron  A  through  a,   or  fron  C  through  c;   both  resections 
should  intersect  in  a  coupon  point  on  be  prolonged:  this  point 
is  d,  the  point  upon  the  nap  representing  D,  the  position  of  the 
observer,  A  circle  through  aec    vrill  also  pass  through  d; 
i.e.    aecd    are  the  vertices  of  the  inscribed  quadrilateral 
discussed  above. 
(252)  The  Triangle  of  Error  Method. 

This  is  also  known  as  Lehnann !s  aethod,  as  an  exhaustive  in- 
vestigation and  discussion  of  this  aethod  has  been  prepared  by 
Prof.  H.  Lehnann  of  the  U.S.  G-eological  Survey,  in  which  it  is 
extensively  used  with  gratifying  results.   By  its  use  the  observer's 
position  nay  be  quickly  and  accurately  mapped,  and  its  use  is 
readily  acquired  by  the  trained  plane-tatle  topographer. 

The  solution  by  this  nethod  (Lehnann1 s)  is  a  simple 
application  of  resection  from,  the  signals  in  the  field  through  the 
plotted  positions  of  the  same  points  upon  the  nap.  As  in  the 


Surveying  1  3, 


Assignment  35 


Page  7. 


other  methods,  the  solution  is  practically  secured  T.vhen  the  nap 
has  "been  correctly  oriented.  You  should  always  bear  in  mind, 
therefore ,  the  necessity  for  correct  orientation  and  the  means  of 
securing  this. 

Figure  107  shows  the 
plane -tat le  set  for 
determining  the  pos  i- 
tion  of  observer  and 
plotting  it  upon  the 
nap.  The  resection 
has  resulted  in  pro- 
ducing the  small 
shaded  triangle  at 


Fig.  107 


t;  but  if  the  map 
had  been  correctly 
oriented,  i.e.  had 


ac  been  parallel  to  AC  (fron  which  it  would  follow  that  ab  was 
parallel  to  AB  and  that  be  was  parallel  to  BC),  then  by  the 
laws  of  geometry  the  lines  through  the  vertices  of  the  two  tri- 
angles ABC  and  abc  oust  intersect  in  a  point;  the  existence  of 
a  triangle  instead  cf  a  point  is  evidence  that  correct  orienta- 
tion has  not  been  secured. 

Hence,  to  secure  correct  orientation:  turn  the  board  in 
azimuth  in  that  direction  which  will  tend  to  dimish  the  triangle 
t,   (called  triangle  of  error)  until  the  resection  lines  have  a 


Surveying  1  B.  Assignment  35.  Page  8. 

common  point  of  intersection.  The  position  of  the  table  in  this 
illustration  is  such  that  the  board  should  be  turned  counter 
clock-wise  in  order  to  accomplish  this  result;  in  other  words 
the  point  d  (plotted  position  of  the  observer)  trill  be  found 
to  the  right  of  the  triangle  in  sone  such  point  as  d  in  the 
figure, 

Yov.  can  readily  verify  the  fact  that  if  the  point  d  were 
to  fall  beyond  the  limits  of  the  nap  that  this  method  or  any 
method  fails.  Again  if  a  circle  is  drawn  through  the  signals  in 
the  field  A,  B,  and  C,  called  the  "great  triangle",  any  sta- 
tion of  the  observer  upon  this  circle  in  the  field  becomes  inde- 
terminate -  i.e.  with  the  observer's  station  at  any  point  on 
this  circle  the  resection  lines  will  intersect  in  a  point  as  the 
quadrilateral  formed  with  A,  B ,  C,  and  D  as  vertices  would 
constitute  an  inscribed  quadrilateral. 

It  may  be  seen  that  in  Figure  107   ,  the  point  D  is 
necessarily  outside  of  the  "great  circle",  as  the  circle  passing 
through  points   A,  B,  and  C  is  called. 

The  solution  is  said  to  be   strong  when  the  observer 
is  in  certain  positions;  these  are  well  outside  of  (or  within) 
the  great  circle,  or  when  the  observer  is  within  the  great 
triangle   which  is  the  triangle  formed  by  the  three  signals. 
Also  the  solution  is  strong   when  the  observer's  station  is 
nearer  to  B  (the  aiddle  signal)  than  to  A  or  C.  Figure  107  , 
therefore,  showing  a  specially  strong  solution. 


Surveying  1  B. 


Assignment  35. 


page  9, 


Since  two  or  three  attenpts  to  determine    jl    may  be  made 
"by  trial,   this  method  is  kno\vn  as  "the  triangle  of  error  method'1. 
The   student  will  find  an  admirable  treatise  on  the  plane-table  by 
D..  B.  Wainwright,     published  by  the     U-S-   Government,  Bureau  of 
Publications,     Washington,     D«C° 

Llano ; s  Method . 

This  method   is  essentially  geometric  and  appeals  to  many 
plane-table  topographers     as  a  direct  and   simple   solution,     con- 
suming little  time  and  giving  results  adequately  exact  for  most 
pur pose s, 


C. 


Fig.   108 


The  plotted  positions  of  a,  b,  c  are  drawn  upon  the  map.  Bisect 
ab   and  draw  a  perpendicular;  place  alidade  on  this  perpendicular 


Surveying  IB-  Assignment  35.  Page  10. 

"bisector;  turn  the  "board  and  sight  B;  resect  from  A  through  a 
and  where  this  line  cuts  the  perpendicular  mark  e;  dravT  the 
perpendicular  bisector  of  "be;  place  alidade  on  this  line  and 
turn  the  board  sighting  B;  resect  from  C  through  c  anc!  mark  f; 
with  £  and  f   as  centers  and  ea  and  fc  as  radii  draw  arcs 
intersecting  each  other;  the  intersection  of  these  arcs  is  d, 
the  plotted  position  of  the  observer.  Verify  this  by  centering 
alidade  on  _d  and  sighting  A,  B,  C.  NOTE:-  The  position  of 
d  may  also  be  found  by  drawing  a  line  from  d   perpendicular 
to  ef ;  this  point  is  as  far  froia  ef  as  the  point  b   is. 

This  method  depends  for  accuracy  upon  the  distance  bet\?een 
e  and  f  ;    when  this  is  small,  the  determination  is  inacu- 
rate ;  if  the  tv/o  points  e  and  f  coincide  the  problem  is  in- 
determinate. 

The  choice  of  methods  is  governed  by  the  conditions  in  each 
case  and  by  the  means  at  hand  for  constructing  the  lines  in  the 
figures.   Practice  and  the  consequent  skill  acquired  by  the  to- 
pographer -will  generally  enable  him  to  choose  a  method  suited 
to  the  case  in  hand. 

All  methods  fail  vhen  the  point  A  falls  off  the  map.  the 
only  remedy  is  for  the  observer  to  change  his  position  to  a  near- 
er station,  or  in  any  case  one  more  favorable  to  the  proper  and 
accurate  solution. 
(253)  The  Two-point  Problem. 

The  observer's  position  may  be  determined  when  only  two 


t  :-  -  ' ':  /:: 


'   •    r 


Surveying  1  B  < 


Assignment  35. 


Page  11. 


points  in  the  field  instead  of  three  are  given.   This  is  known 
as  the  two-point  problem,  and  its  solution  rests  upon  the  assump- 
tion .of  a  third  point  located  "by  the  observer.  This  usually  is 
accomplished  by  setting  up  a  line  (of  the  character  of  a  base- 
line) by  locating  two  points  for  observation,  one  of  which  is  the 
point  sought.   It  is  evident  that  an  understanding  of  this  problem 
is  quite  essential  to  the  efficient  topographer,   since  cases  arise 
when  it  is  necessary  to  use  it.  A  statement  of  the  problem  is  as 

f ollCWS ; 

Given  -  the  location  in  the  field  of  two  points  and  their 
plotted  positions  on  the  map  and  the  station  in  the  field  of  the 
observer.   Required  -  to  plot  the  position  of  the  observer  upon 
the  map. 

Referring  to 
Figure  109,  in 
which  A  and  B 
are  the  points 
in  the  field 
and  T  is  the 
plane-table  on 
which  the  points 
a  and  b   have 
been  plotted  to 
scale  and  the 


Fig.  109 


map  supposedly  oriented.  Assume  _d,   and  intersect  on  A  and  B 


Surveying  1  B.  Assignment  35.  Page  12. 

through  a  and  b  respectively.  Then  move  table  to  C  and 
intersect  on  A  and  B,  through  a  and  b.    The  intersections 
at  a'  and  b '  with  c  and  d  will  form  a  quadrilateral  of  the 
proper  form  "but  incorrectly  placed.  Hence  turn  the  board  through 
the  angle  dcd '  and  resect  again  for  d  (or  c.  if  desired). 

If  a  point  can  be  occupied  in  line  with  the  two  given  points 
A  and  B,  the  table  may  be  set  up  at  this  point,  which  we  may  call 
P  (on  nap  p),  and  the  board  oriented  by  placing  the  alidade  on 
pba  and  sighting  BA  in  line;  then  direct  the  alidade  toward  some 
point  Q  in  the  field  and  draw  a  line  pq;  finally  occupy  Q, 
backsight  on  P  with  alidade  on  :qp  ,  thus  orienting  the  board.  The 
point  q   is  novr  located  by  resecting  from  A  and  B  through 
a  and  b.  This  is  a  quick  and  satisfactory  method  practiced  by 
topographers  under  the  conditions  indicated  above. 

(254)         You  should  understand  that  in  most  plane-table  problems  the 
whole  board  is  regarded  as  a  point,  and,  when  compared  with  the 
large  areas  over  which  such  problems  extend,  it  is  accurate 
enough  to  regard  it  thus.   It  is  well  to  realize  too  the  similar- 
ity  between  the  plane-table  parts  and  those  of  the  transit. 
The  alidade  corresponds  with  the  alidade  plate  of  the  transit; 
the  board,  with  its  movement  in  azimuth,  corresponds  with  the 
lower  plate  of  the  transit,  etc.  Follow  out  this  comparison  and 
note  the  completeness  of  this  agreement  or  similarity.  Realize, 
too,  that  while  the  transit  is  an  instrument  of  refinement  and 
precision,  the  plane-table  is  often  the  more  economical  and 
sufficiently  trustworthy  as  to  results  obtained  by  its  use. 


Surveying  IB.  Assignment  35.  Page  13. 

QUESTIONS  ON  THE  PIAIE-IABIE 

1.  State  the  several  adjustments  of  the  plane-table  and  compare 

them  with  their  corresponding  adjustments  in  the  transit. 

2.  Is  it  necessary  that  the   line  of  sight  of  the  alidade  telescope 

alidade 
an<3Aruler's  edge   lie  in  the  same  vertical  plane?     Give 

reasons  for  your  replies. 

3.  Compare  the  four  methods  of  plane-table  surveying  with  equiva- 

lent transit  methods  for  the  same  purposes. 

REFERENCES : 

Breed  and  Hosmer     Vol.    II,  pp.    191  -  222. 

Tracy     318     to  336 

Johnson  -     Solutions  of  Three-Point  Problem  p.   278  et  seq. 

Raymond  -     Solutions  of  Three-Point  Problem  p.   291  et  seq. 


•  .• : 


UNIVERSITY  OF  CALIFORNIA  EXTENSION   DIVISION 
Correspondence     Courses 

Survey ing- IB  Elements  of   Surveying  Mr.    Swafford 

Assignment  56 

MINE      SURVEYING 

Foreword:     A  brief  treatment  of  the    subject  of  Mine   Surveying, 
including  the  instruments  and  the  -methods  employed  and   some  of  the 
problems  peculiar  thereto^  will  constitute  the    scope  of  this 
assigrrnent . 

The  terminology  and  nomenclature  used  by  miners  and  others 
connected  rith  raining  need  not  be    set  forth  at  length  in  this  con- 
nection; but  a  few  terc.s  and  names  are  here  defined  in  order  to 
avoid  unnecessaty  details  and  circumlocution  in  the  introductory 
part  of  the    subject* 

The  essential  difference  between  the    surveying   subject  already 
dealt  vrith  in  this  course  and  mine    surveying  lies  in  the  fact  that 
in  addition  to   the  usual  problems  we  have  those     relating  to  under- 
ground areas,    shafts,   tunnels,    and    so   forth.       Many  of   the  methods 
and  the   instruments  used  in  the  work  peculiar  to  the  usual   surface 
surveys  are  found   unsuited  or  wholly   inadequate   to   the  proper  or 
convenient  accomplishment  of  underground  work;  while  many  of  the 
problems  of  mine    surveying  differ  materially   in  their   nature  from 
those   of   general   surveying  as  already  treated. 

(255)  A  Few  Terms  Defined :     A  ^haft   is  an  opening  from  the    surface 

downward   into   a  mine;    it  may  be  vertical  or  more   or    less  inclined, 
and   is  not  always   straight.     This  is  used  for  entrance  of  workmen 


••'•''  '<    ---'••-  •••••'•    •••.••:•    .•*••;        '        ; 


.-.- 


'  '-'-•         -  '     ''  •    '    ..       .  :.    .    •'. 


•  v    - '  -": "'. 

..  '    •.:.       -  ••.' 


Surveying- IB.  Elements  of  Surveying.  Assignment  36,  page  2. 

and  others  into  the  mine  and  for  introducing  machinery  and  for  re- 
moval of  ore  or  ether  material.  For  these  purposes  a  bucket  or 
cage  operated  by  cables  and  hoisting  engine  is  used. 

A  tunnel  is  an  opening  into  a  mine  and  usually  extends  hori- 
zontally with  two  openings;  i.e.,  it  passes  through  the  hill  or 
mountain  into  which  it  penetrates,  although  the  term  is  loosely 
used  to  indicate  a  more  or  less  commodious  ingress  into  the  mine 
for  purposes  similar  to  those  of  a  shaft. 

An  adit  is  still  another  form  of  opening  from  the  surface, 
usually  at  the  general  level  of  the  diggings  and  hence  is  often 
called  an  ad it -level.  Unlike  the  tunnel  the  adit  only  opens  into 
the  mine  by  one  entrance  and  has  no  other  outlet. 

On  hillside  diggings  the  adit  or  tunnel  is  the  more  logical 
construction  of  entrance,  it  is  generally  more  easily  and  cheaply 
built  and  permits  of  operations  that  require  a  minimum  of  lifting. 

The  terms  floor,  roof,  and  wall  are  about  synonymous  with 
these  terms  when  applied  to  the  corresponding  parts  of  houses  and 
nay  be  understood  without  special  definitions. 

Collar  is  the  term  used  to  indicate  the  timbers  around  the 
opening  of  the  shaft.  At  the  entrance  of  a  tunnel  or  adit  the  name 
frame  and  timbering  is  sufficiently  descriptive. 

Levels  are  the  series  of  horizontal  wor kings  at  successive 
elevations  or  depths. 

A  connection  is  a  short  passage  connecting  two  or  more  parts 
of  the  workings  on  the  same  or  different  levels. 


...'".  i'    '.:  .!      -I'..'.-:"".-          ,'  .•.;'-."     ..-'..•     .-..-. 
"  • 

"' '  " '  ' 

'     '       '  '  '  '  •         '      '' 

'  ;       •-;•'•          •'         ''     "    "     ' '• 

. 

"  '     •    ..  '  • 


' 

.    .  •         :        .. 

.     .     .       . 


; 
• 

.     •  *  :        '•          .-   .  .    •  -  '    •  •  .      '    '       '  .         "     .      '  •'    '  ;        '  .        ':*     ''   •'  •'•' "•'•      '' 

•••'•-•  .      ••    • '        - 

-'    '  -  •"'.'-          emT 


''-TO' 

' 
.-  .          . 

"-'.':'.'' 


, 


'     '• 


•  :     :  ••  •;  •'.    ••,. 

'     '      :          


Surveying-IB.     Elements  of   Surveying.     Assignment  36,   page  3. 

A  winze   is  a  connection  of  the  nature  of  an  underground    shaft 
that,  while   it  may  connect  trro  or  more   levels,  has  no  exierior 

opening. 

is 
A  vein  is  a   stratum  of  ore;  usually  this/dnibedded  in  rock  of 

a  different   sort  Irom  the  ore   itself,  and  the  workings  are  usually 
directed  along  the  course  of  the  vein. 

Dip  and    strils  are  terms  used  to  define  the  course  of    the 
vein;   dip  means  the  angle  of  inclination  of  the  rock  plane  to  the 
horison;    strilae  is  the  bearing   (or   "cross-country"  direction)  of 
this  rock  plane  in  a  direction     e.t  right  angles  to  the  dip.     A 
horizontal  passage  following  the  vein   is  called  a  dr if t . 
(256)  Liine    surveying  is  from  its  nature  divided  into  two  branches 

differing  more  or   less  widely,    in  that  one  has  to  deal  with  the 
under  ground  work,  while  the  other  deals  with   surface  measures. 
Traverses  are  run  on  the    surface  and  underground  to   locate  and  de- 
fine the  property   lines  above  and  belo"  ground,  to  give  bearing 
and  distances  of  tunnels,    shafts,   connections,  drifts,  etc.     Depths, 
slopes,  and  azimuths  are  determined  with  the  greatest  accuracy 
possible,  and  these  must  be   connected  with  the   surface   survey  by 
lines  measured  in  angle  and  distance  with  careful  precision.     To 
accomplish  this  a  meridian   (true  or  magnetic)  or  a  line  of  known 
azimuth  is  carried  fron  the    surface  into  the  underground  works. 
The  Eiethoda  for  doing  this  will  be  given  further  or.  in  this 
assignment. 


.  .  .  -       -..-•-.      .  •  •-          • ..  . 

...      .       .:•-;;.:. 

•'"'•'.      -  •  •  ••  • '     •  •'   '-• -      •      ' 

•'  '     .          -  •  '        .'•-.••;..         :  •  '..•••.. 

'.;.':'  '     •      •        '"•   -•••'   •• 

•     •     .        .....:        ...•..;:.:,-.:    -      .    ; 

-     ••    '•  --:"  '••-     -     '  "•' :'  "      '•    " 

.    •  '-•  -  •      .      :••      •  -  -:     ,.:-•/        : ....  •      .-..:.-  :        ;  '.  •' 

•     ••  ; .    .'  .       ... 


•  -  •  ....      .       •...:.•/  -s  •.':-•.     .       •':;'.'      ...  -...;  •-,-..      . 

'.    -•  :;  -  -   '••       .       •         •:::••.. 

-  '   -       '       ••  ;• 
•  -  ... 

.  ; .  : 


Surveying- J.3»     Elements  of  Surveying.     Assignment  36,  page  A» 

In  the   IO*.T  underground  passages  in  mines  we  meet  conditions 
that  differ  greatly  from  those  found  on  the    surface.     First  of  all 
the   light  is  much  fainter ,   often  amounting  to  total  darkness,   ex- 
cept for  the  artificial  illumination  which  is  mostly  poor  and  al- 
v;ays  insufficient  for    surveying  purposes.     Therefore,   lights  are 
used  for    signals  and  suitable  lanterns  for  reading  rods,   gradu- 
ated circles,   and  for  record  ng  notes  and  reading  maps,  records, 
etc. 

Since  the  passages  have   low  roofs,   often  only  a  few  feet  in 
height,    it  is  necessary  that  rods,  tripods,   and  other  instruments 
should  be    short,   or,    as  in  case  of  tripods,  6f  the  extensible  pat- 
tern.     In   some  cases  it   is  convenient  to  mount  the  transit  head 
upon  a  bracket   screwed  into  the  wall  or  to  place  it  upon  a  tr  ivet , 
a   sort  of  very   low   support  having  three  feet,   hence  the  name. 

The  presence  of  tracks  upon  rAiich  «ars  are  run  for  trans- 
porting the   ore,  or  the  travel  of  men  and  animals  over  the  floors 
of  the  passages,  renders  the   setting  of  points  thereon  impractica- 
ble in  most   cases;   hence  hubs,  points,   and  even  monuments  are 
placed  if  possible   in  the  roofs  or  upon  the  walls  of  rooms  and  pas- 
sages.    This  necessitates  the   suspending  of  plumb-lines,   not  from 
the  transit,   for  example,   but  above  the  transit  which  is   set  up 
underneath,  the  point  of  the  plumb  bob  centered  over  a  point  coun- 
tersunk in  the  telescope  axle. 

Plummet   lamps  or  candles  may  be  used  for    signals;   or  a 
screen  of  paper  or  cardboard  makes  a  good  mark  when  illuminated 


'   '      '  "      '      '  *'-•    ;       •'  3+  •  -•'••  •...-    ::•;.  »V  •      ••••.  -•-.... 

""'      ;"        '  i:-    '       •""-•••:  "•'••••:•.;::/.•;,•     ••:--.•.     ..     .   .- 

:'  "  '        '"•'  T '•'":'• "    •  •  ':••'          -.  •     •      -..-.-  V         -  ;  ..     .   > 


"   ';  '".    •'  :  '       '•-•  '•"'  •    '';     "      :    -  -.-/       i-:   •:..-. 

''    '    "    ''    '    T      "^  '•"        •       :     •  •'     ••--•  •    •  ..-      --    •  -•    $?..;      ....    . 


7         -    ••  '•'      -'  ••"  •  ''-^    -:  ;>  >-;    ;-.-.     • 
•  -   -;     --':-  '••    '•  &    '::.    .;;  ;     ...••.      :-.,      .,  .  .   :.;    . 


'•'-'•  "-  .-  '      ~'-:'"'-    •   '•    •'"'••  •'••"•    --,.:/.  :•...:-      . 

•    --'       V-'-'   V-.-  ;:     .J-s_-  : 

*   "    '  -  •'      "  '    "'.•'     '-...•  -..-         '•     '.- 

"'    ""       'i~   '    '"'r ' "-     "•"  •      :.  ?;•.*.      •     :       •      .      ...        •  . 

•  •  -  -       .'  •     '".,'.  "•..-    .;..;•   .      •.  *  •-       c  .1 

'      •'    •  '''•••'  •":  •- :-   .'         ..-..   .-•  

'••    •'    •-     '•••':        •-',.'. 

'      "  7     '"     '   '"":  '  :        '      •  •  :      '  ••:      ••-•    -  ..  •'•'  •. 

'  "•:    '••  •:-  -•  ^:  .  ,;  .-V  -. ._,     ..  _  .  ..../. 

'  "    "'    ""    '     "       '  '  •       ''"':'    •'•••:.-       .....  ^       .       ;.••.. 

"•       ••••""  :  -  --.•:=•.        ... 

•        • "  .         :  •  ."       -  (      '  . 

,  ••'••:  ;•,;..'  ..      ••••     ... 

•    '    "  '  ' '  '" " :    "';-  '       '  ..;•'.•;.•;. 

.-•••--.  --..  .  -  -  .  . 


'  •  '•'  '  -      .        :  •  •,•    V>-;U-i-l';i    ;.. 


Surveying-IB.     Elements  of  Surveying.     Assignment  36,  page    5. 


by  a  suitable  light.     The  transit    should  be  fitted  with  a 

ting   shade,    so  that   light  from  a  torch  or   lamp  may  be  reflected 

dovm  the  tube  for   illuminating  the  cress  hairs  in  the  tsle  scope. 

(<?£?/,  The  transJ.t  for  underground  work  should  i>e  of  a   substan- 

tial but   light  pattern.      It   should  have  a  large  objective  arid  a 
low  magnifying  power,   as  sights  are  usually   short  and  much  light 
rather  than  magnification  is  preferable.     Either  the  erecting  or 
the  inverting  type  may  be  used,  the  choice  depending  upon  the  user, 
but  the  inverting  type  possesses  many  advantages. 

A  full  vertical  circle  is  essential  as  the  instrument  is 
frequently  plunged.     The  vertical  circle    should  be  ivell  protec- 
ted by  a  cover   guard,  hence  double  verniers  are  convenient.     As 
it   is  often  required  to   sight  vertically    (or  at  great  inclina- 
tion)  either  upward  or  downward,  the  transit   should  have  either 
a  top  telescope  or  a  side  telescope  to  enable  the  transitman  to 
look  past  the  plates,  vAiich  is  impossible  with  the  ordinary  trans- 
it  in  case  of  greatly  inclined  sights.     The  instrument   should  al- 
so be  fitted  with  a  prismatic  eye  piece  for  use  with  large  verti- 
cal angles. 

(258)  The  top  telescope  above  mentioned  consists  of  an  auxiliary 

telescope  attached  over  the  top  of  the  main  telescope  at  a   short 
distance  from  the  main  telescope  equal  to  the  radius  of  the  hori- 
zontal base  plate  and  a  little  more  to  permit  of   sighting  past 
the  plate.     The  auxiliary  is  attached  best  by  two   short  columns 
connecting  the  two  telescopes,  but   several  forms  of  attachment  are 


• 

•'  ••     '..  . 

1  -     '•'••''• 


" 


.    ,:  ./...      ;-••   .-.;.  -•        ... 

"•:      ••-  — •    *•    .'  ••./  v  . . 
-'  •  '  ":-  'wo'S-   J»- 

'   -  •';  -'7"  .::.v..;  ••   ':     •  ' 

;  •    ••  '••-•" 

•    '  ••-:-----'  '-   tg  .   • 
•         -     •.,       ;•>'.  -_-; ..::  j-  .    ••     ;    •  - 





'":    :"      "    "';     -v'"'--- 


Surveying-IB.     Elements  of  Surveying.     Assignment  36,  page     6» 

made* 

The  side  telescope  is  also  an  auxiliary  telescope  fastened 
to  the  side  of  the  main  telescope  but  usually  in  the  case  of  this 
latter  auxiliary  it  is  screwed  to  the  axle  of  the  main  telescope 
and  rigidly  fixed  thereto,  so  that  it  may  always  turn  with  the  main 
telescope,  both  remaining  in  the  same  plane  with  the  horizontal 
axis»  It  is  distant  enough  to  clear  the  base  plate  of  any  project- 
ing screw,  and  is  properly  counter -balanced  by  a  weight  attached 
to  the  axle  at  the  opposite  trunion. 

(259)     Measuring  angles  when  sighting  with  the  top  telescope  may 
be  understood  by  the  following  consideration: 

The  top  telescope  and  the  main  telescope  are  fixed  in  the 
same  plane  with  the  vertical  axis  of  the  instrument,  the  lines  of 
sight  of  the  two  telescopes  are  parallel,  and  they  are  at  a  defi- 
nite knovm  distance  apart,  called  the  eccentricity;  hence,  all  hori- 
zontal angles  measured  by  use  of  either  the  auxiliary  or  main  tele- 
scopes are  the  true  horizontal  angles;  vertical  angles  are  differ- 
ent in  the  two  cases,  the  angle  of  error  in  reading  with  the  top 
telescope  being  equal  to  the  angle  whose  sine  is  the  distance  of 
a  point  from  the  instrument  (horizontal  axis)  divided  into  the  ec- 
centricity of  the  telescope. 


. 

'•    --..-•  :/,  -  *4  '--<'•:  -H-- -    •:••::<  '•  •:. 

' 


•••••••••• 


' 


...   _•  .....  -.-!•-,••       .••>;;..•;•••-. 
"5  ".•••':  ••.-.'••»•    <-i'%>J    •  «  •    -•    •  •      •—•---•- 
•  --------  •-'••' 


. 
':    :•':.:    l».j-^*I*-!    •:-'v"     -  ''       ;/':  :      fsi>***s  '        V"'    ''"":: 

• 
-  -  r,-.:- 


.,         . 

- 


. 


•••          ...        . 


.-_  ...    ;.:T    u;iWV    U  :f^:      .:;  ''    '  " 

'• 


;.-r.u-v:  fa   W.*/   '«    *!>*«   •••••    tr-*     - 

. 

' 

' 


Suvveying-lB.      Flemeats  of  Purveying.     Assignment  36,      page     7. 


Fig.    110 


Fig»  j.10    shows  a  transit    set  upon 
an  eminence  from  which  it   is  de- 
sired to  measure  the  a.ng?.e  of  de- 
pression by  means  cf  the  top   tele- 
scope,   and  to   compute  the  height 
N    (N)   and  the  horizontal  distance 
OP. 

Sighting  the  point  P  with  the  top 
telescope,   read  the  angle    O\   on 
the  vertical  circle;  measure  the 
slope   distance  HP.      But  this  gives 
a  false   angle  of  depression  inas- 
much as  the  top  telescope  must  be 
depressed  more  than  the  main  tele- 
scope  in  order  to    sight  P,   and  the 
angle   LRP  is  the  true  angle  of  de- 


pression which   is  greater   than  IMP;   hence   LHP  -  IMP   is  a  correction 
angle  to  be    subtracted  from  DRP.     This  angle  has  for    sine,  E    (the 
eccentricity)   divided  by  MP    (the   distance  from  the  horizontal  axis 
to  point  P).       Now  angle  MPO  is  equal  to  the  true  angle  of  depres- 
sion and  OP  =   LAP. cos  MPO  and  OM  =  MP»sin  MPO. 

Tc  facilitate   computations  a  table  of  values  for    sin   (p-c<) 
at  varying  distances  MP  may  be   compiled.     The   eccentricity  E  being 
a  constant,  the    sine  of  the  correction  angle  varies  inversely  as 
the    slope   distance  MP. 


"•""  •  '    "  '--'"•  ;  •     '  '••'• " •'"'  '•  '• "    " 

;..    •.'.-.  -.     .:       •-.-•:    .      .       .•."-•. 


'"--"•       -'•  -      '    ••'     •• 

;  .'-...  •::••-  -,,     -....  - 

•-.-    ..     •.•.:.     ;-.;•  ':    .,.--•    :•:  vl 

.   i     '••'•   -"-"'     -':  •   -:X'S- -'•    -:    ?  ;.  -: 

-  ...;    :.:•.•   •  .  .\    :    ":-•-    M:  ..     ..   •-  .'  . 

•  :-;/    ''•       '    r*  i»  r  •'•-•••    :-:'  •• 

:~''*     •-•'--    "••     -'-•-   ;-•..•••.• 

;.;     '   •-        ,/•     •:  ;     :  :      f    •     |^   f-j    ."  '     |  ;;'   '. 

.•:          --.  :    :• ..   •    :  ::  •        •  •  .       •-  -..    j, 

.  •.          •          .        ....    .          ..,..,.%    -, 


'- '  ••- 


Surveying-IB.     Elements  of  Surveying.     Assignment  36,   page   8. 


(260)         The  following  considerations  will  make  clear  the  use  of  the 
side  telescope   in  measuring  angles. 

The   side  telescope  and  the  main  telescope  are  fixed  in  the 
saiae  plane  with  the  horizontal  axis  of  the   instrument,   the   lines 
of   sight  of  the  two  telescopes  are  parallel   in  this  plane,   and 
are  at  a  definite   known  distance  apart    (the  eccentricity  in  this 
case);   hence,   all  vertical  angles  measured  by  either  the  main 
telescope  or  the    side  telescope  are  true  vertical  angles;   but 
horizontal  angles  read  by  the    side  telescope  are  false  angles  of 

azimuth  and  must  be   corrected  as  follows: 

/V  „ 

Fig.    Ill    shorvs 

how  azimuth  may  be 
corrected  when 
horizontal  readings 
are  made  with 
pointings  of  the 
side  telescope. 
Sightings  are  made 
on  B  and  F  with 
the  auxiliary  tele- 
scope,  but   the   angle   required   is  BCF;   as  the   angle  turned   in  read- 
ing with   the   auxiliary   is  BXM  it   is  plain  that  this  value   is  in- 
creased by   SBC   (=£?)   and  diminished  by  FXIvi   (  =  ot);   hence  the   true 
angle   at  vertexAis  FXM   -    p  +CC.      Here  (3     =  angle  whose   tangent   is 


Ho.  /// 


Surveying- IB  Elements  of  Surveying.  Assignment  36,  page  9. 

E  *  CB,  andoC  =  angle  whose  tangent  is  E  *  CF,  E  being  the  eccen- 
tricity. When  CE  =  CF  no  correction  is  required. 

(261)  Solar  observations  for  meridian  are  best  made  by  direct 
observation  upon  the  sun,  although  the  usual  forms  of  solar  at- 
tachment may  be  used.  But  the  combined  solar  and  top  telescope 
attachment  is  not  recommended. 

The  compass  in  mine  surveying  is  of  little  use  as  an  instru- 
ment for  taking  azimuths  or  bearings.  The  presence  of  iron  ores, 
machinery,  rails,  and  lighting  and  pov;er  lines  for  electric  energy 
rail  practically  preclude  the  use  of  the  compass  in  this  sort  of 
-::orlc. 

(262 )  REIAJIOH  OF  SURFACE  MD_  UNDERGROUND  SURVEYS 

For  the  purpose  of  connecting  the  surface  and  underground 
areas,  it  is  necessary  that  a  common  meridian  be  carried  from  sur- 
face into  the  v/or kings.  This  may  be  accomplished  by  one  of  several 
means.  The  meridian,  or  a  line  of  known  azimuth,  may  be  carried 
directly  into  the  underground  area  through  a  tunnel  or  an  adit;  to 
do  this,  it  is  only  necessary  to  prolong  a  line  of  the  surface  into 
the  mine  through  the  adit  or  tunnel,  or  to  carry  a  line  of  conveni- 
ent bearing  out  of  the  tunnel  and  determine  its  bearing  or  azimuth 
with  respect  to  some  known  line  of  the  surface  survey. 

The  method  of  carry ihg  a  meridian  into  a  mine  through  a 
shaft  will  depend  upon  the  nature  and  size  of  the  opening  and  pos- 
sibly too  upon  the  depth  of  the  shaft.  Plumb  lines  may  be  dropped 


.       ._  .  . .      .  .      .  .    : 


. 

•    •       '  -  -  •  -  -••      '•      <-    -  '.     '1 

3    h ...  .....    . 


-  •:  ...    .••..,..,  .:.;.:•:... 

.....  ...  :      .....  •         ' 


. 

. 
~  •  '  '-:     '•    -•' '•'•     «•'*      •'•     »."•.»  ~\    •         ..-"    ..  -V-Vr      .-'      ~l  .'.-'     ;v  IVV   ..     :  -'     • 

..... 

T  "I.".  /...'.."    ".".      "- '    '.'...':      .'....:»       *•',.."  ":•;  ' 
... ,    ..  ..    ..     ...;...       .     . .  .     ._-,_.     t  .      ... 

•     .  .  ...  ..;  C    ,.        ..,     .  . 

....  ...         .      .  ...  :..,..-...  ,..  .  ; 

.-•'   .•  :    -.•  .  •:   .•-.-•:•  :  --:  >    :.    •  ••       •••.:".-      ~  .  ^ 

.......      »,  ..    ....      ...      -.         .  .    .  .    ,. 

-  -  .  -  -   •  -    • 


Surveying-IB.  Elementary  Surveying.  Assignment  56,  page  10 

from  two  points  upon  the  collar  and  the  "bearing  of  the  line  con- 
necting them  determined;  this  is  practicable  when  the  shaft  is 
verticle,  so  that  the  plumb  lines  hang  free  of  the  walls,  and 
the  opening  is  wide  enough  to  allow  of  a  line  of  sufficient  length 
between  the  two  points. 

In  case  there  are  tvro  shafts  the  latter  difficulty  is  removed; 

points  may  be  established  at  the  bottom  of  each  shaft  by  plumbing; 

connecting  line  on  the  surface  is  then  the  azimuth  01°  the 
the  azimuth  of  ihe^line  joining  the  t-"o  points  below. 

(263)      A  transit  vith  auxiliary  telescope  may  te  used  for  the  purpose 
of  carrying  a  meridian  into  the  mine  through  a  diaft,  and  in  case 
the  shaft  is  inclined,  this  is  the  most  feasible  means. 

Set  up  the  transit  at  a  convenient  place  at  the  mouth  of  the 
shaft;  backsight  on  a  suitable  point  on  the  surface  "fith  telescope 
plunged;  right  the  telescope  and  set  a  point  at  the  botton  of  the 
shaft,  if  possible,  as  far  as  practicable  within  the  mine.  Read 
the  angle  (deflection,  as  described  below)  and  calculate  the  azimuth. 
Occupy  the  point  below  and  set  off  the  back  azimuth  sighting  the  point 
at  the  collar,  and  from  this  position  lay  off  a  line  of  convenient 
length  in  the  mine,  determining  its  azimuth. 

Too  great  care  cannot  be  given  to  the  matter,  as  much  depends 
upon  the  correctness  of  the  line  -  all  lines  of  the  under prouna 
workings  are  connected  therewith  and  a  small  error  may  be  multi- 
plied or  at  least  repeated  again  and  again. 


'  i  -••• 


;  •->:  •.-  •   ::  -•-  '  "-• 


••».•*    •"    •••'=•-- 


Surveying- IB.     Elementary   Surveying.     Assignment  36,  page   11. 

(264)  The  distance  dorm  a   shaft  is  measured  by  tape;    if  inclined, 
by    supporting  the  tape  at  points  along  the   inclined    side;   or   if  the 
shaft   is  vertical,  by    suspending  the  tape  and  putting  the    same  under 
tension  by  hanging  a   known  weight  upon  it,      If  the  tape  hangs  free 
the  tension  of  the  tape  will  be  W-frwl/2,  where  W  is  the  attached 
weight,   w  is  the  weight  of  a  linear  foot  of  tape,    1  is  the  length 

of  the  tape  under  tension.     The  tape  may  norr  be  compared  with  a 
standard  by    supporting  both  tapes  throughout  their   length  and  ap- 
plying the  tension  above  determined.     Very  deep   shafts  may  te  Trea- 
sured by  means  of  a  piano  wire,  which  is  afterwards  compared  with 
standard  in  like  manner . 

(265)  Many  measurements  of  distance  are  necessary  or   conveniently 
made  from  the  head  of  the  transit  instead  of  from  a  point  below  the 
plumb   bob  and  care  must  be  taken  to   secure  the  correct  measure. 
Again,    since  many  points  are  chosen  upon  the  roof  or  walls  of  rooms 
and  passages,    it   is  frequently  necessary   in  talcing  angles  of    slope 
to    such  points  to  reckon  the   "height  of  point"  as  veil  as  the  height 
of  instrument.     The  H-I.  may  be  positive  or  negative  depending;  uoon 
its  position  with  respect  to  the  transit;    if  the  point  from  whi^h 
the  H-I-    is  taken  is  below  the  transit,    it   is  positive    (•*•);    if  above 
the   transit,    i.e.  measured  downward,    it    is  negative    (-)•      Likewise, 
the  "height  of  point"   (K.Pt.)   is  positive  when  measured  from  above 
downward  and  negative  when  measured  upward.     Due  regard  to  these 
quantities  and  their    signs  is  of   special  import  in  reading  angles 

of   slopes- 


. 


. 

•  •      •  -•    •         .  -     "•     • '  -          -  " 

"... 

..."  .  • 

.     "  "•:.""' "        •        '        '  '     • 

'.••••     '.'..       -'     ;  •"<••:""-..'  X-     .  .----.    . -.;    ;;;;,_    -- 

"•    "T     • 

'-•      B-.  -•      «•      •-.  ••        *• '    -»'•-    :,  ""       •-       ....-!    ' 

• 

" 


- 

"-T          -    "  :»V<        -tr--  ;  Kfe-    .,.' 

' 


Surveying-IB-  Elementary  Surveying.  Assignment  36,  page  12. 

(266)     Ir.  running  traverses  at  surface  and  underground  they  should 
be  connected  by  starting  at  a  common  initial  point  and,  if  possible, 
closing  upon  a  point  common  to  the  two  traverses*  The  two  traverses 
thus  run  will  be  open  traverses  but  the  closing  line  of  one  will  be 
identical  with  the  closing  line  of  the  other;  hence,  by  computing 
this  closing  line  for  each  of  the  two  traverses  a  reliable  check  may 
"be  secured.   In  case  the  two  traverse sArun  from  a  common  initial 
point  cannot  be  closed  on  the  same  point,  then  the  closing  line 
of  each  traverse  is  comupted  and  from  the  data  thus  secured  a 
closing  line  between  the  two  is  then  also  computed,  but  it  is  evi- 
dent that  no  check  is  possible  in  this  case. 

Fig.  112  illustrates 
a  surface  traverse,  A12B 
and  an  underground  traverse 
A345B,  beginning  at  A  and 

B 

closing  on  B.  Here  it  is 
required  to  find  the  dis- 

s 

tance  AB.     This  can  T>e  done 

T 

by  finding  the  missing  part, 

AB  and  its  bearing  (See  Assignment   18,   on  supplying  missing  data). 
The  traverse  A12B  furnishes  the  necessary  data,  as  also  the  traverse 
A345B;   the  v-.lue  of  AB  by  the  trro  routes  should   check. 

To  illustrate  any  case  where  the  common  point  of  closing  is 
wanting,    see  Fig.    113.     Here  the   line  MN  is  computed  for  the   surface 


-  v.-*/:. 
•--  -  •       •,.•". 

•    •     :      "  I     '       V 

« 

-.-•  .  ':  -   .:- 


,....-  994',      • 
:...    -.^ 


.    -•      :--.     3*    ::'      .. 


•     -        ;•.."."=:. 
r-  -',:.;  ~    --• 


.  :    .       : 


•   ':    ~-  •  . 


:  -  •  ••'•_    .-•'  .  - 


Surveying- 13.     Elementary  Surveying.     Assignment  36,  page   13. 


M  "> 


traverse  M12W  and  this  line  is  then  taken  as  a  part  of  the  under- 
ground (incomplete)  trav- 
erse M3450NM  -  and  the 
line  NO  computed  by  the 
method  of  supplying 
omissions.  In  this  case, 
however,  there  is  no 
check  upon  the  work  and 
all  lines  and  bearings  must  therefore  be  measured  with  scrupulous 
exactness. 

(267)     Mining  Claims:  The  surface  extent  of  mining  claims  is  de- 
fined by  the  U.  S.  Government,  and  these  limits  must  not  be  ex- 
ceeded by  claimants,  although  the  limits,  less  than  these,  are 
sometimes  regulated  by  local  (State)  laws. 

Coal  mine  and  placet  claims  are  20  acres  in  extent,  by  U.  S. 
Government  regulation,  and  mineral  (lode)  claims  are  defined  as 
1500  feet  along  the  strike  of  the  lode,  either  in  a  straight  or 
broken  line,  and  extending  300  feet  at  right  angles  to  this  line 
en  both  sides.  The  end  boundaries  are  required  to  be  parallel  to 
each  other. 

The  following  diagram,  Fig.  114,  will  further  show  the  form 
of  a  mineral  claim  as  defined  by  U.  S.  Government  laws,  for 
regulating  same: 


. 


• 

. 


. 
•'-•'• '    '•• .: 


- 


' 
«  -.  ;  •  r  .-;    •  '  f       .  ;.••  • 


• 


Surveying-IB.     Elementary   Surveying.     Assignment  36,  page 


£  \     ^  V 

...-"•* y 


A/£ 


C1 


S£ 


The  place  where  the  prospecting  was  conducted   is  shown  at  M; 
from  here  a  line  is  run  N60°  10 fE  to  0  where   it   is  made  to  deflect 
12°  05'  R   (or   its  bearing  from  this  point   is  N  72°  15 '  E)  thence 
to  C1;   the   line   is  also  run  from  M,   S  60°  10'  W  to  C,  the  total 
length  of  the  center   line  COC1    is  1500  feet;    suppose  the  bearing 
of  the  end  line  Sit  to   NW  is  N  20°  00*  W,  then  the  other  end 
boundary  must  also  bear  N  20°  OO1  W,    i.e.,  the  end  boundaries  must 
be  parallel;   the    side sboundary   lines  may  be  300  feet   (perpendicular 
distance)   on  each  side  of  the  center   line   COC1. 

These   lines  and  dimensions  may  be   laid  out  by  the  prospec- 
tor or  claimant  and  the  approximate   location,   and  necessary  witness 
marks,    such  as  stakes,  bearing  trees,   etc.,   described  by  the  clai- 
mant in  filing  his  claim;   an  official    survey  is  not  required  for 
this  purpose. 

Subsequently  before  a  patent  can  be    secured,   it  is  necessary 
that  an  accurate   survey   shall  be  made  by  a  qualified  Mineral  Land 


"       :  •  -        ':i---.      .-    •       : 

'.'..:       -•..•       .-.':.-•:        '*  • 


-    -•  •          ---•   .--'.  '••  :  "  •  •      -.-•   .,'•  .- 


.;     .•:..-.    :.•     -     ;.—   : 


•'-    -  .- 

•       •-.-..        .      --.-.'      :.        .;..._•      q.      .-. 


.  '     ..•••••...          -.     :.   .. 


Survey ing- IB.     Elementary  Surveying.     Assignment  36,  page   15. 

Surveyor,   and  ii-  is  upon  his  report  that  a  patent  is  issued. 

The  official    surveyor  is  not  rigidly  bound  by  the  claimant's 
survey,  but  he  aims  to  follow  consistently  the   lines  and  points 
previously  established  when  these  conform  to  good  practice  and  do 
not  interfere  with  the  rights  of  other  claimants  or  established 
surveys. 

The    survey  must    show  the  relation  to  any  existing  U.    S. 
Land  Survey  in  the  region  where    situated.     This  is  usually  done  by 
giving  the  true  bearings  of  the  boundary  lines  of  the  claim,   and 
at  least  one  corner  of  the  claim  is  tied  to  a   section  or  quarter 
section  corner  where  possible. 

The  Deputy  Mineral  Surveyor   is  a  regularly  appointed  official 

•+0  inswvc. 
and  is  under  bond  with  severe  penalties  £or   the  faithful  performance 

of  his  duties. 


REFERENCES: 


Breed  and  Hosmer,  Vol.    1,   pp.   321-371. 
Johnson  --------       Chap.  XI 

Raymond   --------        Chap.  XII 

_,.-*-*-*-*-*- 


•    '        '  •;       '     :  '        .•-    -..    ••:•',    '•       •''••          •-•   '•  ''•  '•-  '•     •    '-'  --?-"- 

...  -  .    •  .  •         •  ;       .•  ..;•...'.••" 


• 


Surveying-IB.     Elementary  Surveying.     Assignment  '66,  page  16. 

PROBLEMS: 

1.  A  transit  v.'ith  top-telescope  was  used  to   set  a  point  down 
an  inclined  shaft;   the  angle  read  on  the  verticle   circle  was 

58°  18'.      If  the    slope  distance  from  the  horizontal  axis  was  312.5 
feet,    and  the  eccentricity  of  the   auxiliary  telescope  was  0.33 
feet,    (a)  ^//hat  was  the  correction  angle,   and  what  the  true  angle 
of  depression?      (b)  what  was  the  horizontal  distance?      (c)  what 
was  the  vertical  distance? 

2.  It  is  required  to  measure  the  angle  ACB  with  a  transit 
equipped  with  a   side  telescope,    set  up  over  the  point  C;    sights 
were  taken  on  A  and  B  with   side  telescope  and  the  angle  read  on  the 
vernier  plate  was  61°  38*>    if  the  distance  from  C  to  A  was  212.3 
feet,   and  from  C  to  B  187.6  feet,   and  the  eccentricity  of  the 
auxiliary  telescope  was  0.31  feet,  7/hat  were  the  correction  angles 
and  the  true   interior  angle  ACB? 

3.  A  mining  claim  is  1500  feet  along  the  center   line,   and  in* 
eludes  300  feei  parallel  thereto  on  either   side^  and  is  furthef 
described  as  follows:     The  place  of  discovery,  M,    is  450  feet 

S  80°  GO1  E  of  the  west  boundary  of   said  claim  which  boundary   is 
made  at  right  angles  to  the  center   line  of  the  claim;  600  feet 
east  of  the  west  boundary  the  center   line  deflects  left  23°  15*. 
Lay  out  the   claim  on  a   scale  one  inch  equals  300  feet,   drawing  the 
bounding  lines,  the  center   line,   and   showing  the  bearing  and  dis- 
tance of  each   line. 


•  ..  -•  :   •''••  -~  • 


•  - 


•  •     -  •-•  -'     '••  -  .      -  •:       *- 

-  ••   t-   •'•'"  -••  '••   ••  -  !.    -;:;. 


---'         •..;•/  -        --    ;-:.- 


'•"•••        "        '  t  ~!  -  '      •        '••-'"'  "'  '*"-"••;   '•'."'.''•'-•.    :'-   •• 

'"••  •         ' ' :,-.    ". :.'  :..'  -     ••     . "..  • 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 

Correspondence  Courses 

Surveying-13         Elements  of  Surveying       Mr.  Swafford 

Assignment  37 

Hydrographio  Surveying 

Forward:  The  purpose  in  this  assignment  is  to  isrive  somo  of  the 
methods  in  that  snecial  branch  of  topographic  surveying  known  as 
"Hydrographio  Surveying".  We  will  not  presume  to  enter  upon  an 
elaborate  treatment  of  the  subject,  but  to  give  rather  the  problems 
and  methods  met  v;ith  in  the  ordinary  work  of  surveying.  Only  those 
problems  which  employ  the  usual  tools  of  the  surveyor  will  be  dis- 
cussed, with  perhaps  the  addition  of  a  few  of  the  simpler  but  in- 
despensable  instruments  required  for  such  work. 

( 23G )     Scope  _pf  the  Subje  ct : 

Hydrogra.phic  Surveying,  although  properly  classed  as  topographic  sur- 
veying, is  more  particularly  regarded  as  a  highly  specialized  branch 
of  the  sv.bJTct.  In  all  of  its  problems  it  deals  with  water,  water 
surfaces,  depths,  streams,  etc.  Hence  any  survey  that  has  to  do 
with  seas,  lakes,  harbors,  rivers,  and  other  aqueous  bodies  is  classed 
as  hydrographic,  and  the  surveyor  is  here  confronted  with^problems 
calling  for  treatment  peculiar  to  each  case,  but  concerned  always 
with  water,  either  in  quiescent  form  or  flowing.   The  intimate  relation 
to  land  topography  will  generally  be  apparent. 

(259)  Prpb_lens_o_f  the_  ^Subject 

A  fev;  of  the  pr&blems  net  with  in  hydrographic  surveying  are: 


Surveying-IB.  Assignment  3V,  page  2. 

(a)  The  i.ieasuranent  and  mapping  of  the  coast  lines  of  lakes,  ponds, 
and  seas;  (b)  the  Determination  of  the  forns  of  sub-aqueoi-i.s  areas 
covered  by  them;  (c)  the  courses  and  depth  of  channels,  presence  and 
location  of  submerged  rocks,  reefs,  and  shoals;  (d)  the  rise  and  fall 
of  tides;  (e)  and  the  flow  of  streams,  their  slope,  nature  of  channel, 
change  of  channel,  velocity  of  flow,  and  the  quantity  of  discharge 
and  its  nature. 

The  scope  of  the  sxi.bject— its  methods  and  problems— are  indeed 
of  prodigious  importance  and  often  call  for  highly  specialized  treat- 
ment.  They  must  therefore  not  be  considered  of  trifling  nature  sug- 
gested by  this  passing  view  of  elementary  phases  of  the  work;  the 
student  should  realize  that  very  often  vrorks  and  structures  of 
irmense  importance  and  involving  intricate  engineering  undertakings 
are  dependent  upon  the  survey  conducted  in  many  cases. 

To  enumerate  again:   The  many  kinds  of  engineering  ventures 
depending  upon  a  hydrographic  survey  are:  the  improvement  of  harbors, 
erection  of  lighthouses,  building  of  sea-walls,  dredging  of  rivers, 
buildin-;  of  bridges,  dams,  tunnels,  drainage  of  areas,  and  numerous 
other  works. 
(270)  Survey^  of  Shors-line: 

"..rhen  it  is  desired  to  survey  the  shore-line  of  a  lake  or  bay, 
for  example,  and  this  for  the  purpose  of  determining  its  boundary  or 
for  inclusion  upon  a  map,  it  is  the  practice  to  run  a  traverse  at 
a  convenient  distance  from  the  shore-line  upon  the  land,  and  to  then 
establish  the  requisite  number  of  points  for  defining  the  low-water 


Surveying-IB.  Assignment  37,  page  3. 

shore  of  the  body  of  water.  This  traverse  is  generally  of  the  open 
type,  but  even  in  such  a  case,  though  the  closing  course  of  the  traverse 
cannot  be  measured  directly,  it  is  often  desirable  and  expedient  to 
secure  a  closing  line  by  stadia  or  by  triangulation,  since  such  line 
would  afford  a  valuable  check  on  other  elements  of  the  survey. 

If,  as  often  happens,  the  coast-survey  is  an  integral  part  of 
other  topographic  features,  which  have  been  based  upon  a  triangulation 
systen,  then  in  turn  a  suitable  net  is  projected  to  furnish  the  re- 
quired basis  of  the  hydrographic  portion;  or  a  special  base,  in  some 
instances,  is  carefully  established  and  the  triangulation  then  pro- 
ceeds from  this  base  by  the  usual  methods  to  include  the  hydrographic 
features  sought. 

If  a  traverse  has  been  run,  off-sets  are  then  taken  from  des- 
ignated points  on  the  traverse  lines  to  the  points  on  shore  at  as 
frequent  intervals  as  the  character  of  the  coast  may  require.  These 
points  may  be  measured  by  tape  where  great  accuracy  is  required  and 
the  nature  of  the  ground  may  permit,  or  by  stadia  when  a  lesser 
degree  of  accuracy  is  allowable  or  the  intervening  terrain  renders 
direct  measurement  inconvenient  or  impossible; this  might  be  neces- 
sary on  account  of  intervening  marshy  stretches,  or  where  precipitous 
rocks  stand  in  the  way  of  chaining.   Triangulation  must  sometimes  be 
resorted  to. 

The  illustration,  Fig. 115,  will  show  the  combined  methods 
along  a  coast-line,  consisting  of  a  portion  of  a  bay.  Here  the 


Surveying-IB,  Assignment  37,  page  4. 


E 


Wearing  and  Distance  by  Transit  and  Stadia 
Fig.  115 

transit  points  A  to  Z  am  located  at  convenient  distance  from  the 
shore-line  (exaggerated  in  the  figure)  and  perpendicular  off-sets  are 
shown  by  dashed  lines;  through  the  .points  thus  determined  the  law- 
water  line  SSSSS  is  drawn.  The  line  AE,  shown  by  a  b roken  line,  is 
conveniently  found  by  stadia,  and  its  bearing  and  distance  also 
computed  by  latitudes  and  departures,  as  a  check  upon  other  elements 
of  the  traverse.   The  points  A,  B,  C  would  conveniently  be  located 
by  triangulation  from  X  and  Y,  two  triangulation  stations  of  the 
land  topography.   The  bearing  and  distance  of  each  course  of  the 
traverse  is  found  by  transit  and  tape,  or  by  transit  and  stadia. 
Besides  the  careful  sketch  shown  here  (drawn  approximately  to  scale), 
a  full  set  of  notes  in  tabular  form  is  kept  and  the  distances  along 
the  transit  lines  to  off-set  points  as  also  the  lengths  of  off-sets 


Surveying-IB,     i.ssignruent  37,  page  5. 

are  also  tabulated.   From  such  data  a  faithful  map  of  the  coast 
is  drawn. 
(271)  Soundings. 

The  measurements  of  the  depth  of  bodies  of  water  are  called 
soundings  and  are  made  at  specified  points  over  the  water  surface 
for  the  purpose  of  determining  the  nature  of  the  sub-aqueous  area. 
The  work  is  v.sually  carried  on  from  a  boat  by  means  of  poles  or 
lead-lines;  if  the  former,  a  stiff  narrow  rod  of  wood,  generally 
weighted  at  the  lower  end,  and  graduated  in  feet  and  tenths  is 
used.  In  shallow  water  rods  up  to  15  feet  in  length  graduated  as 
described  may  be  used  to  advantage,  but  longer  rods  are  difficult 
to  handle,  and  even  with  the  shorter  rods  much  decterity  is  required, 
especially  in  vater  in  motion  from  currents  of  tidal  flow. 

For  depths  greater  than  two  fathoms  (l  fathom  =  6  feet)  lead- 
lines are  employed.  These  consist  of  hemp  cords,  3/8"  to  1/2"  size, 
carrying  a  lead  weight  at  the  lower  end,  weighing  5  to  20  pounds. 
The  cord  is  suitably  marked  by  tags  at  each  foot  and  half-foot 
interval,  after  being  wet  and  stretched,  so  that  the  shrinkage 
caused  by  wetting  is  in  a  measure  eliminated.  As  this  precaution  is 
only  temporary  in  character,  s.nd  is  likely  to  be  affected  by  long 
use,  the  line  and  its  graduations  should  be  tested  from  time  to  time 
by  comparing  with  a  standard  length,  as  a  tape  or  the  distance  be- 
tween two  fixed  points  on  shore. 

Leads  are  of  several  forms  depending  upon  the  purpose;  one 
form  has  a  cup-like  cavity  at  the  lower  end,  which  is  designed  to 


Survey ing- IB.  Assignment  37,  page  6. 

lift  a.  small  quantity  of  the  bottom  material,  from  which  the  character 
of  the  sub-area  may  be  judged- — this  may  be  mud,  gravel,  sandy  sludge; 
or,  in  the  absence  of  "sample",  it  would  indicate  rocky  formation. 
When  samples  are  especially  desired,  the  cup-like  cavity  is  smeared 
with  tallow  (called  greasing  the  lead)  to  which  the  bed  materials 
will  more  readily  cling.  A  more  elaborate  device  has  a  cup  suspended 
at  the  bottom  of  the  lead  by  a  short  stiff  bar  and  a  leather  cap 
sliding  upon  this  bar, acts  as  a  cover  to  prevent  the  sample  from 
washing  out  as  the  lead  is  raised, 

As  the  sounding  proceeds  it  is  necessary  to  locate  the  point 
of  each  sounding.  This  may  be  done  in  various  ways.  The  position 
of  the  boat  nay  be  measured  "off-shore  "  by  observing  the  angle  by 
means  of  the  sextant  and  afterwards  computing  the  distance  from  known 
signals  on  shore.  For  this  purpose  it  would  be  necessary  to  have 
four  men,  or  more  depending  upon  the  kind  of  boat.  Supposing  that 
the  boat  is  propelled  by  a  single  oarsman  then  the  crew  should  con- 
sist of  a  leads-man,  a  recorder,  an  instrument  man;  the  recorder 
may  also  serve  the  tiller,  if  the  boat  is  thus  equipped. 

The  leads-man  is  stationed  in  the  bow  and  the  man  handling  the 
sextant  is  immediately  behind  him,  the  oarsman  occupies  the  middle 
seat  and  the  recorder  sits  astern. 

Another  method  requires  the  reading  of  angles  from  stations 
ashore.   This  is  done  by  two  transit-men  with  instruments  set  up  at 
known  points  that  are  intervis5.ble  and  that  command  a  clear  view  of 
the  water  area  over  which  the  soundings  are  to  be  taken. .  This  is  in 


Surveying-IB.  Assignment  37,  page  7, 


M 


reality  the  method  of  tri:mgulatio:i  so  common  in  topographic  work 
generally.  Fig.  116  shows  points  M,N,0,P  connected  bTr  triangulation 

to  a  station  T,  the  azimuth  and  dis- 
tance of  which  are  carefully  determined. 
AS  the  soundings  A B C  are  in  pro- 
gress the  transits  a  re  set  up  first  at 
11  and  ^,  each  sighting  first  on  each 
other;  then,  at  the  instant  a  sounding 
is  taken  both  sight  upon  the  leads- 
man's station  simultaneously;  the  moment 
of  taking  the  sounding  can  be  signaled 
from  the  boat  by  means  of  a  flag. 
The  transit-men  then  move  to  N  and  0, 
""2.  \    and  again  taking  stations  0  and  P. 
This  is  a  very  accurate  and  satis- 
factory method,  but  of  course  involves 
considerable  equipment  and  two  transit-men  which,  of  course,  means 
expense. 

If  the  soundings  can  be  taken  in  range,  vrhich  is  expedient 
v-hen  a  profile  of  the  bottom  of  a  stream,  or  bay  or  harbor  is  re- 
quired, then  the  method  requiring  no  transit  is  feasible.  This  is 
.one  as  follows:    Two  oosts  are  planted  in  range  with  the  desired 
course  of  sov.ndingc;  the  posts  are  erected  so  that  they  may  always 
be  kept  in  view  from  the  boa.t  from  which  soundings  are  taken.   It  is 
well  to  have  these  signals  painted  white  or  some  other  bright  color 
that  is  in  ocntrast  with  the  back-ground  against  which: they  may  be- 

/ 

viewed  from  the  boat. 


Fig.  116 


Surveying-IB.  Assignment  37,  page  8. 

The  sounding  party  in  the  boat  keep  these  signals  in  range 
rowing  in  as  nearly  a  uniform  rate  as  practicable,  and  taking 
soundings  at  regular  time  intervals;  thus  the  depths  at  approximately 
equal  intervals  are  obtained.  The  profile  may  now  be  plotted  in  this 
particular  range*  If  other  profiles  are  desired,  the  range  may  be 
altered  accordingly. 


Problems. 

I,  The  following  data  are  those  shown  in  Fig.  115,  page  4. 
Course   Bearing  Distance 

A-B   N  50000'  E  340.0  ft. 

B-C   N  90°00'  E  320.0 

C-D   S  58°00'  E  240.0 

D-E   S  0°00'  E  280.0 

Required,  the  bearing  and  distance  of  E-A.  If  A  and  E  are  inter- 
visible,  how  may  the  bearing  and  distance  be  measured  directly? 

II.  Referring  to  Fig.  116,  page  7,  the  following  data  are  given. 

TN  *  730.0  ft.,  TO  =  680.0  ft.,  Angle  NTO  =  SS'OO1,  Angle  NOB2  »  75°00', 
Angle  ONB2  =  40°00'. 

Required  the  distances  NO,  OB  ,  NB  . 

*-     £ 


UNIVERSITY  OP  CALIFORNIA  EXTENSION  DIVISION 

Correspondence  Courses 
Surveying-13        Elements  of  Surveying        I.Ir.  Swafford 

Assignment  38 
Mapping  and  Office  V.[ork  -  Computing. 

Foreword'; 

The  work  in  this  .assignment  will  consist  of  mapping  problems: 

1st,  A  Profile  of  River  Crossing;  2d.  three  traverses,  each  by  a 
different  method,  r.ll  to  be  placed  upon  one  sheet;  3d,  A_  Topographic 
Juap_,  in  which  the  data  given  and  worked  out  in  detail  ir.  Assignment 
33  will  be  voade  available.  You  are  specially  xirged  to  make  this  a 
particularly  profitable  set  of  exercises,  and  to  follow  the  directions 
given  to  the  least  detail.  These  exercises  will  serve  as  an  index 
of  your  attainment  in  the  vrork  of  the  course,  and  will  further  dis- 
play your  aptitude  for  carrying  out  projected  work  and  your  mastery 
of  the  important  details  of  officev/ork  in  connection  with  field 
data. 

Consult  all  references  available  and  such  other  sources  of 
information  on  drawing,  mapping,  and  lettering  as  may  be  likely  tc 
contribute  to  your  successful  completion  of  the  projected  maps. 

In  order  to  prevent  the  maps  from  becoming  folded  or  danaged 
in  the  mails,  send  them  to  the  Extension  Division  in  a  substantial 
mailing  tube. 
rl&terial; 

For  the  three  mapping  problems  the  following  material  is  re- 
quired which  may  be  purchased  from  the  Xeuffel  and  Esser  Co., 


Surveying-IB.     Assf.gnr.ent  38,   page   2. 

30  Second  St.,  San  Francisco,  or  from  the  A  Lietz  Co.,  61  Post  St., 
San  Francisco. 

Approximate  cost. 

1  yard  Plate  A  Profile  Paper  20"  wide.         $0.25 

2  ;-ards  Detail  Paper  36"  wide.  .40 

1  yard  Tracing  cloth  36"  wide.  .45  ^ 

Total  $1.10 

This  does  not  allow  for  enough  extra  to  use  in  case  one  sheet 
is  damaged,  so  proper  care  should  be  exercised  to  prevent  mistakes 
in  inking,  etc. 

Mapping  Problem  1. 

Profile. 

For  this  problem  use  2  ft.  of  10  in.  Plate  A  profile  paper. 
Plot  the  profile  of  the  stream  crossing  given  in  the  notes  below. 
Horizontal  scale  1"  =  20* ,  vertical  scale  1"  *  41.  Place  station 
0  so  that  the  profile  is  well  spaced  on  the  sheet.  Y/rite  the 
elevations  on  the  horizontal  lines.  At  each  alternate  heavy  verti- 
cal line  write  the  station  number  just  below  the  lowest  horizontal 
line. 

Profile  of  Lorenzo  River  Crossing. 


Sta. 

Elev.      Remarks 

Sta. 

Elev.      Remarks 

0+00 

158.6 

2+10 

125.5 

+10 

157.5 

+15 

126.3 

+15 

157.2 

+25 

129.7 

+22 

156.8 

+30 

130.5 

+30 

155.2 

+35 

130.6 

+4-0 

154.2 

+40 

130.3 

+48 

152.8 

+  50 

129.0 

+59 

150.0  high  water  1907 

+60 

127.4 

Surveying-IB.  Assignment  38,  page  3. 

Sta.     Elev.      Remarks          Sta,     Blev.    Remarks 


+75 

148.3 

+64 

126.8 

+90 

147.0 

+76 

126.8 

+95 

147.1 

+90 

129.0 

1+00 

146.8 

3+00 

130.3 

+05 

145.6 

+08 

131.0 

+10 

146.3 

+20 

131.6 

+20 

146.0 

•r35 

133.0 

+24 

145.7 

+50 

134.8 

+32 

145.2 

+60 

135.8 

+36 

141.2 

+75 

137.8 

+48 

140.4  ore  sent  water  level 

+80 

140.4  present  v/ater  level 

+70 

133.0 

+90 

148.1 

+82 

IS0.2 

4+00 

151.8 

+86 

128.6 

-:-10 

153.9 

+95 

124.9 

+20 

155.5 

2+00 

124.8 

Plot  the  profile  jLifthtly  in  pencil  (profile  paper  will  stand 
very  little  erasing).  In  plotting  each  point  place  the  pencil 
point  on  the  plotted  position  and  drav;  tack  to  the  preceding  point 
a  free  hand  straight  line.  Smooth  out  this  broken  line  when  the 
profile  is  inked. 

Before  inking  you  should  check  the  profile  carefully  and 
send  it  to  the  Extension  Division  for  the  approval  01"  your  instructor. 
For  inking  use  a  contour  pen  or  a  ball  pointed  pen,  making  the  line 
about  the  same  width  as  the  heaviest  lines  of  the  profile  paper. 
Ink  the  profile  in  black.  Place  the  following  standard  form  of"  title 
in  the  upner  middle  part  of  the  drawing: 

University  of  California 
Extension  Division 

Plane  Surveying    Assignment  30 

Profile  of  Lorenzo  River  Crossing 

(  Name  ) 


Scales:   1  in.  -  20  ft.  horizontal 
1  in.  -  4  ft.  vertical 


Survey ing- IBB.  Assignment  58,  page. 4. 

Great  care  and  much  taste  raust  be  exercised  in  lettering, 
especially  in  titles.  Use  guide  lines  and  slope  lines  and  a  simple 
letter  of  uniform  style. 

Mapping  Problem  2. 
Traversejs. 

General  Instructions.  Use  detail  paper  20"  x  21''  with  standard 
border  as  indicated  on  page  8  of  this  assignment.  Make  the  finished 
sheets  18"  x  24"  with  border  3/41'  inside  those  dimensions.  Considering 
the  north-south  line  to  be  parallel  to  the  shorter  side  of  the  draw- 
ing, let  the  origin  of  plotting  coordinates  be  at  the  lower  left 
(3W)  corner  of  the  border  line. 

Complete  the  entire  drawing  in  pencil  and  return  it  to  the 
Extension  Division  for  the  approval  of  your  instructor.  Do  not 
do  any  inking  of  the  drawing  until  it  has  been  approved  in  pencil 
form.  Check  it  over  very  carefully  before  submitting  it. 

There  are  three  traverses  to  be  plotted  on  the  one  sheet. 
The  scale  for  each  traverse  is  l"  =  2001.   Shew  directions  and 
length  of  every  course  in  each  trc.verse  as  in  Blueprint  Problem  3, 
Assignment  6,  (or  Figure  199,  Breed  and  Hosmer).  Use  standard 
north  point  illustrated  at  the  end  of  this  assignment  and  the 
form  of  title  already  indicated.  (C.E. Traverses  -  Chord,  Tangent 
and  Protractor  Methods).  Place  the  title  in  the  lower  right  hand 
corner  of  the  plate.  Use  soft  pencil  for  lettering  so  that  erased., 
mistakes  will  not  shov;  by  reason  of  indentation  of  the  paper. 


Surveying-IE,  Assignment  ?8,  page  5. 

TRAVERSE  "An 

Traverse  "A"  will  be  plotted  by  deflection  angles,  using  the 
tangent  method.  The  deflection  angles  will  be  computed  from  the 
notes  given  below.  Reference'-  Assignment  30,  p.  3;  Breed  &  Hosmer; 
Arts  490-491.  Show  in  this  traverse  plot  a  typical  construction 
for  a  deflection  angle  less  than  45?,  and  one  for  a  deflection  angle 
between  75°  and  90e. 
Sta.     Deflection      Bearing  Distance  (ft.) 

pr  6°  37'  W 932.4 

. N16  43     E 500.0 

N  2  36    •£ 1018.0 

. K78  53     E 664.9 

.  .  .325  57     E 900.6 

.  .321  26     W 468.1 

S10  22     E 938.7 

. S45  23     W 579.4 

, N87  57     W  - -  -  715.3 


Note:   Co-ordinates  Sta.  A  (270.0  N,  340.0  E) 

Check  deflection  angle  and  bearing  closure. 


TRAVERSE  "B" 

Traverse  "Br!  vd.ll  be  plotted  by  laying  out  the  bearing  angle 
of  each  course  by  the  chord  method,  drawing  a  north  and  south  con- 
struction line  through  each  transit  point.  The  bearings  are  to  be 
computed  from  the  following  notes.  Reference :  Assignment  30,  p.  5; 


Surveying-13.    Assignment  38,  page  6. 

Arts.  492-494.  Show  in  this  traverse  a  typical  construction  for 
a  bearing  angle  less  than  45°  and  one  for  a  bearing  angle  between 
75°  and  90°. 

Sta.    Deflection  Bearing  Distance (ft.) 


N  26°  38'  W 1171.3 

(        ) 722.9 

(        ) 1065.0 

(        ) 679.0 

(        ) 1015.0 

(        ) .  .  1180.0 

(         ) 955.2 


Note:  Co-ordinates  of  Sta.  B  (430.0  N,  1925,0  E). 

Check  deflection  angle  closure  and  bearing  closure. 


TRAVERSE  nC" 

Traverse  "C"  will  be  plotted  with  a  141'  paper  protractor, 
using  azimuths  from  the  south  point  which  will  be  computed  from 
the  following  notes.  Reference :  Assignment  30,  pp.  6-8;  Breed 
&  Hosmer;  Arts.  481-483. 
gjba.       Deflection          Azimuth          Distance  (ft.) 

C, 73°  35'   R 

' 159°   10' 635.0 

C2 32   15    R 

" (       ) 455.1 

C3 9   15    L 

(       ) 410.3 


B! 

41°  30' 

R 

Bi 

72  15 

R 

B3 

59  25 

L 

B4 

100  00 

R 

5 

66  6.5 

R 

BS 

50  28.5 

R 

B7 

27  10 

L 

B8 

116  15 

R 

B, 


Surveying-IB-   Assignment  38,  page  7. 


Stn.       Deflection          Azimuth  Distance  (ft.) 

C4 61°  40'  R 

(:  ) 468.0 

Cg 124  29.5  L 

(  ) 516.9 

Cg 126  4.5  R 

(  ) 460.2 

C? 32  50-  R 

(  ) 870.8 

Cg 91  45  R 

(  ) 918.1 

CQ 29  15  L 

(  ) 596.0 

C,0 34  40  R 

(  ) -450.1 

C^ 70  10  R 

~  _ (  ) ..  1048.0 

C! 

Note:  Co-ordinates  of  Sta.  C^  (72)  .0  N,  3300.0  E) 
Check  deflection  and  azimuth  closure. 


Happing  Problem  No.  3. 
Topographic  Mapping  Problem 

Traverse.  The  field  notes  'for  the  traverse  to  be  used  in 
connection  with  this  problem  have  already  been  included  in  Assign- 
ment 33.  In  this  assignment  you  were  required  to  compute  horizon- 
tal distances,  differences  in  elevation,  and  elevations;  and  to 
balance  the  traverse,  adjusting  the  elevations  and  distributing 
any  closing  difference  in  proportion  to  the  lengths  of  the  respec- 
tive sides. 

Map.  Using  the  traverse  commutations  indicated  plot  the  traverse 
by  the  co-ordinate  method,  checking  by  scaling  the  lengths  of  the 
sides,  -'rite  in  pencil  on  the  map  the  length  and  bearing  of  each 


Survey ing- IB.  Assignment  ?8,  page  8. 

side.  The  ruap  is  to  ba  plotted  on  a  scale  of  l"  =  60*,  contour 
interval  5  ft.,  on  detail  paper  of  good  quality,  outside  dimensions 
16"  x  24".  Use  3/4"  margin  and  standard  border.  Assume  the  true 
north  parallel  to  the  shorter  edge  of  the  border,  and  be  careful 
to  select  the  position  of  the  origin  of  co-ordinates  in  such  a  way 
as  to  center  the  drawing  upon  the  sheet.  The  title  is  to  be  placed 
in  the  lower  right  hand  corner  of  the  sheet,  and  is  to  be  of  stan- 
dard form.  The  map  is  to  be  completed  _in  pencil  only  and  sub- 
mitted co  the  instructor  for  approval.  Do  not  erase  correct  con- 
struction work  on  the  pencil  drawing,  either  before  or  after  approval. 
Use  a  411,  or  harder  pencil  for  plotting  traverse  and  side-shot 
points  and  a  softer  pencil  for  drawing  contours  and  for  lettering. 

A  tracing  in  ink  upon  tracing  cloth  (using  the  dull  side) 
is  then  to  be  made  of  the  approved  map.  Tracing  and  original  are 
taen  to  be  submitted  to  the  instructor,  together  with  computations 
and  tabulations.  For  details  consult  references  listed  below  and 
those  given  in  Assignment  33. 
References: 

Breed  &  Hosmer  Vol.  1,  Chap.,  XI  and  XVII;  Vol.  II,  Chap.  XI. 

Tracy  Chap.  XI. 

Raymond  Chap.  XII,  also  plates  1-3,  7. 

Hote:   Bear  in  mind  that  the  originals  of  all  three  mapping 
problems  are  first  to  be  submitted  to  the  Extension  Division 
in  pencil  only  for  the  approval  of  your  instructor.  They  will  .then 
be  returned  for  inking-in  and  should  be  re-submitted  in  final  form 
for  the  proper  grade. 


Surveying-IB.  Assignment  38,  page  9 


Standard  Border  and  North  Point 


- 


: 

/ 


• 


• 


s^111 


UNIVERSITY  OF  CALIFOKWU  EXTENSION  DIVISION 

Correspondence  Courses 

Surveying-IB.       Elements  of  Surveying       Mr.  Stafford 
Solutions  to_  Assignment  _38. 


pjL:t£jjLon.s  ?or  Iviapping  'roslea  2. 


>ba.  Deflection  Bearing  Tangents  Distarce(ft.)    Cotar 

A^ (G1020'   R)  G.5606  0.1524 

-  -  N  6°   37'  T:  0.1160 932.4 

A2   (25°20'R)  0.4314 

_ ________  jjfi5     43     £ __„_ _     500.0 


A4  ----   C76°3.5'r:) 


4     ..   ---   (75°10'R) 


Ag  ----  (AG^.O'R) 


(14°C5'L)  0.2509 


6  ----   (47'25'R) 


A?   ----  (31°50'L) 


A8  ----   (55°45'R) 


I  ----  (81°20TR) 


K  2     38    E  -  -  •    ---    ----  1018.0 

4.  0867  0.2441; 

7578      53     I  .-..  .   -------     S54.9 

3.7760  0.254( 

S25     57     E  -------   -    ----     900.6 

1.0881 
S21     28     W  -----------     463.1 

0.6208 

S10     22     I]   ----------       938.7 

1.4687  0.330S 

5A5     23     W  ----------     579.4 

1.0599 

U87     57     T.T  ------  *  ---     715.3 

6.5606  0.1524 


Note:   Co-ordinates  Stc..  A  (270.0  N,  340.0  E) 

Check  deflection  angle  and  bearing  closure. 


Surveying-IB.  Solutions  to  Assignment  38,  page  2, 


Right 
81°20' 
23  20 

76  15 
75  10 
47  25 
55  45 
46  40 
405  55 


Check 


Larft 
14'OS1 
31   50 
45   55 
360  00 
,405   55 


Sta. 


Deflection       Bearing;      Chords 


B-, 41°   30'   R 

N  26°   38'  W         0.4606 

B2 72     15     R 

—  I TJ    i*1^        *^*7       T?  1  fl    *7  7  c\  9 

'      •"      •••"      ••      —      ««  ^  W      *^;0  O  I  &  J  W  •  f   •  O  tf 

B3 59     25     L 

___ •  _(N  13     48     W)        € 

B4 100     00     R 

Bg 66        6.5  R 

Bg 50     28.5  R 

B?  -  -  -   27     10       L 

(S     4     23     E)        0.0766 

Bg 116   15     R 

(N  68     08     W)        1.8532 

En  II  26      38     W          0.4606 


Pi stance (ft.)  Sin  oC 

2 


0. 


.0 


722.9 


756.4       0. 


0. 


0. 


0.9381 
0.2303 


Surveying-IB.    Solutions  to  Assignment  38,  page  3. 

Note:   Co-ordinates  of  Sta.  BX  (430.0  N,  1925.0  E) 

Check  deflection  angle  closure  and  bearing  closure, 


Right 

Left 

41-301 

59°25l 

72  15 

27  10 

100  00 

86  35 

G6  06g 

360  00 

50  2&| 

7  446  35 

116  15      ^  Check  -""^ 

***^ 

448  35 


_Sta_. 

C      -  -     73?   351   R 


0 


-  -     32     15     R 


C5  -  -       9      15     L 


-  -     61     40     R 


Azimuth      Pi s tan c  e  (ft.)  Bear ings 

159°10' 635.0  ft  2C'050!  V' 

(191  25) 455.1  N  11  25  E 

(182  10)       410.3  N  2  10  E 

(2-13  50)        438.0  I!  63  50  E 


C5  -  -  124     29.5  L 

~-  ........   (US   2Q& 

36  -  -   125     4.5  R 

i  -------    -    -  -  (245   25) 

Gr,   -  -     32     50  R 

i 

------    ..    ---   (278   15) 


516.9       N  60 


430.2  N  65   25  E 


870.8  S   81  45  E 


Surveying-IB .   Solutions  to  Assignment  33,  page  4. 

-£"£.'    Def loction     Azimuth     Distance  ( f  t . )    Bearings 
C8 91°  451  R 

(  I0°00)     918.1  S  10°00!Vr 

CQ 29  15  L 

_.  (340  45)     596.0  S  19  15  E 

C-,c 34  40  R 

(15  25)     450.1  S  15  25  W 

C  . 70  10  R 

- (85  35)    1048.0  S  85  35  W 

C]_  159°10' 

Note:  Co-ordinates  of  Sta.  C^  (720.0  II,  3300.0  E) 
Check  deflection  and  azimuth  closure. 


Azimuths  Deflections 

Az  q  15S°  10'  Right 

V  32  15  R 

**  "•*" "  73°  35 

C2   191  25   -..  32  15 

C3   182  10  12S  04-| 

61  40  R  32  50 

34    243  50  91  45 

1  9A   9Q-^-  T 
X^T:    cy  p  Lt 


c.   119  20-;> 

126  04-g-  R 

C     245  25 

32  50  R 

C?    278  15 


70  10 


91  45  R  Check 


370  00 

560  0 

C      10°  00  '  , 

29  15  L  522°  59^' 

C9    240  45 

34  40  R 

375  25 

360  00 


Surveying-13.   Solutions  to  Assignment  38,  page  5. 

Azimuth s ,  con, 

Clo    15°  25' 

70  10  R 

C11    85  35 

73  35  R 

C1    159°  10*    Check 

liapping  Problem  No.  3. 

For  computations  of  Happing  Problem  No.  3,  see  those  furnished 
with  Assignment  33, 

Included  with  Assignment  38  are  the  following  maps:  Profile  Map, 
Traverse  ilap  ana  Computations,  Topographic  Maps  (pencil  original 
and  tracing)  and  computations. 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 

Correspondence  Courses 
Surveying- IB     Elements  of  Surveying         Mr.  Swafford 

Assignment  39 
Rights,  Duties,  and  Privileges  _of  the  Surveyor , 

Foreword: 

The  title  of  this  assignment  implies  the  fact  that  the 
surveyor  in  the  pursuit  of  his  work  is  vested  with  certain  rights  _.• 
peculiar  to  his  profession  and  that  he  is  accorded  privileges  that 
might  be  wanting  to  one  not  engaged  in  such  work  as  he  may  be  called 
upon  to  do;  also  that  he  is  obligated  by  the  quasi-official  character 
of  his  calling  to  perform  certain  functions  in  a  v/ay  and  to  an  extent 
perhaps  not  required  of  others.  There  are  certain  delicate  and  diffi- 
cult relations  between  the  surveyor  and  his  client,  things  he  owes  to 
the  latter  and  to  himself.  There  are  some  obligations  to  the  employer 
or  the  public  of  which  he  must  be  conscious  while  performing  his 
duties,  and  he  must  endeavor  always  to  place  himself  four-square 
with  his  work.  Let  us  quote  in  this  connection  from  the  introduction 
to  the  course,  Assignment  1,  Page  Q: 

To  properly  accomplish  the  work  of  his  chosen  profession, 
"The  surveyor  must  be  a  man  at  once  honest,  sincere,  dependable, 
energetic,  ingenious,  and  observant.  He  must  be  patient  in  his 
work  and  with  other  people.  He  must  be  ready  to  give  an  unbiased  , 
opinion  as  to  the  rights  of  disputants  when  called  upon  to  do  so, 
and  should  always  be  sure  of  the  correctness  of  his  work  or  its 


Surveying- IB.  Assignment.  39  Page  2. 

limitations  before  submitting  results  to  his  employer  or  to  others 
concerned.  He  must  have  a  thorough  knowledge  of  the  fundamental 
principles  of  surveying  such  as  will  enable  him  to  solve  all  his 
problems  correctly." 

It  will  hence  be  the  purpose  in  this  assignment  to  follow 
the  outline  as  suggested  by  the  foregoing. 

• 

The  surveyor  nust  be  just  in  his  decisions,  and  he  must 
observe  ?.  balancing  of  claims  by  rival  parties.  Fairness  should 
always  be  the  governing  motive  in  all  disputes,  since  the  surveyor's 
work  is  often  for  the  purpose  of  settling  controverted  cle.ims. 

The  nere  fact  that  one  has  the  knowledge  or  skill  that 
makes  him  a  surveyor  does  not  vest  him  with  authority  or  judicial 
functions.  His  training  ought  rather  to  give  him  a  fair  understand- 
ing of  the  limitations  that  beset  the  practice  of  his  profession, 
and  lead  him.  to  a  moderate  view  of  his  importance.  His  functions,  apart 
from  ths  fa.cts  that  his  labors  in  any  case  have  discovered,  are  ad- 
visory; therefore  he  should  be  a  good  councillor  ra'ther  than  a  judge. 
Men  vri.ll  listen  to  his  counsels,  but  few  would  accept  his  decrees. 

The  surveyor  must  also  distinguish  carefully  what  privileges 
are  his,  what  rights  he  ruay  claim,  and  what  duties  he  must  perform. 
He  is  a  servant,  an  agent,  an  officer  in  some  cases  with  duties  fully 
sot  forth  by  statute;  he  must  be  punctilious  in  the  performance  of 
these  duties,  but  must  at  the  same  time  avoid  assuming  those  that 
are  distinctly  not  his;  he  must  modestly  attend  to  his  business — 
his  own  and  not  that  of  others. 


Surveying-IB.  ^ssigmaent  39  Page  5. 

In  other  words  he  must  not  trespass.  This  is  a  strong  word, 
but  trespassers  are  sometimes  punished  for  their  offenses  when  no  of- 
fense was  intended,  and  the  surveyor  is  peculiarly  placed  in  many 
instances  while  endeavoring  to  perform  his  duty. 

A  surveyor  may  pass  through  or  over  lands  of  another  in 
making  neasurenents,  but  he  must  not  commit  any  nuisance  or  destroy 
any  property,  such  as  crops,  trees,  or  buildings;  in  case  any  in  - 
fringnent  of  property  rights  is  made  the  surveyor  is  liable  for  tres- 
pass and  may  be  punished  therefor. 

It  is  often  convenient  to  remove  trees,  brush,  etc,  from  a 
line  cf  road  or  other  survey;  but  this  can  be  done  only  by  permission 
or  by  securing  a  right  of  way.  Growing  or  standing  crops  of  any  sort 
come  under  the  same  rules. 

A  surveyor  should,  in  the  absence  of  permission  to  cross  any 
property  where  damage  by  himself  or  assistants  might  result,  devise 
some  method  of  determining  distance  or  bearing  of  line  or  other  data 
by  v/hich  it  is  unnecessary  to  enter  the  property. 

Railroads  and  private  roads,  canals,  etc.,  usually  secure 
right  of  way,  or  at  least  an  option  promise  carrying  with  it  the  prop-  - 
•er  permit  to  enter  the  property  for  the  purposes  of  surveying.  In 
such  cases  the  duty  (morally)  of  the  surveyor  is  evidently  to  do  as 
little  damage  as  possible  to  crops,  timber,  and  other  property. 

In  the  public  land  surveys,  over  public  property,  the  sur- 
veyor may  exercise  a  wider  liberty,  but  this  should  j^ever  be  construed 


Surveying  -IB  Assignment  39  Page  4. 

to  mean  v/anton  destruction  of  timber  or  crops.  When  in  a  public 
land  survey,  or  that  of  a  highway,  it  is  necessary  to  enter  or  cross 
private  lands,  the  surveyor  is  justified  only  so  far  as  is  absolutely 
essential  in  removing  or  destroying  property,  but  the  employing  prin- 
cipal, the  state  or  county,  or  municipality  may  be  required  to  satis- 
fy any  just  claims  for  damage  committed  by  such  work.  Here  also  the 
surveyor  is  to  avoid  wanton  waste  or  damage. 

The  surveyor's  duty  respecting  all  surveys  conducted  by  him 
is  to  do  all  vrork  vith  the  full  purpose  of  securing  ample  data,  the 
making  of  suitable  sketches  for  his  own  guidance  and  that  of  others 
who  may  come  to  use  the  material  gathered  by  him. 

Notes  must  be  full,  clear  and  complete;  they  must  not  pre- 
sent any  ambiguity  ,  or  otherwise  doubtful  matter;  figures  must  be 
clear  and  plain  so  as  to  afford  a  ready  interpretation;  the  data  re- 
corded in  the  notes  must  show  no  alterations  or  erasures;  If  perchance 
incorrect  quantities  are  entered  in  the  notes  and  the  necessary  alter- 
ations are  to  be  made,  it  should  be  done  by  crossing  out  the  erroneous 

entry  and  writing  above  (or  below)  the  correct  quantities.  In';  case 
a  sketch  is  made  to  accompany  tabulated  quantities,  the  lengths 
(distances),  bearings  (angles),  and  other  related  parts,  such  as  names 

of  ovmers  of  adjoining  property,  cardinal  directions,  etc.,  must  be 
indicated  in  proper  place  and  in  suitable  form  on  the  sketch,  thus 
connecting  the  sketch  with  the  tabulated  data  which  it  is  desired  to 
illustrate  and  clarify. 


Surveying-13  Assignment  39  Page  5. 

Throughout  this  course  your  attention  has  repeatedly 
been  called  to  the  forms  of  notes  approved  for  various  cases;  other 
forms  are  made  use  of,  and  in  some  cases  a  different  form  may  recommend 
itself,  but  a  careful  consideration  of  form  is  a  matter  of  importance 
in  all  cases.  Remember  that  notes  of  surveys  are  generally  made  for 
others  than  the  surveyor  himself  to  use— to  read  and  readily  and 
clearly  xmderstnad;  hence,  any  departure  from  approved  form,  any 
omission  of  important  data,  or  the  absence  of  sketch  and  explanatory 
notes  may  lead  to  much  confusion,  and  the  work  of  the  surveyor  may 
be  rendered  worthless  through  faulty  or  insufficient  notes. 

A  practice  of  so;ae  surveyors  of  purposely  suppressing 
important  data,  or  necessary  directions  or  explanations  in  order  that 
they  may  monopolize  a  survey  when  made,  is  to  be  deprecated;  this  is 
a  species  of  dishonesty  seldom  met  with,  but  instances  are  common 
enough  to  v/arn  the  novice  to  avoid  any  practice  so  flagrantly  unfair — 
unprofessional.  This  brings  us  to  consider  an  important  matter,  which 
is  the  ovmership  of  surveys. 

If  the  surveyor  has  acted  in  the  capacity  of  an  employee, 
servant,  or  agent,  i.e.  has  done  the  \vork  for  hire  and  has  received 
compensation  for  his  services,  evidently  the  product  of  his  labors 
connected  therewith  belong  to  the  employer.  Hence  the  right  to 
monopolize  the  results— the  notes,  data,  maps,  or  information 
gathered  for  the  purpose  belong  to  the  one  who  pays  for  the  survey. 
If  such  a  one  is  a  private  individual,  to  him;  if  it  is  for  a  company, 


Surveying- IB  Assignment  3S  Page  6. 

firm,  or  corporation  the  rights  of  ownership  are  vested  in  the  company, 
firm,  or  corporation.  Under  this  last  classification  may  come  a  muni- 
cipality, county  ,  or  state,  and  in  such  case  the  survey  becomes  a 
public  document  and  should  be  made  a  matter  of  record. 

In  making  a  survey  the  following  things  should  be  carefully 
attended  to: 

1.  The  bearings  of  all  lines;  preferably  the  true  bearings; 
but  if  the  magnetic  bearings  are  given  instead,  then  the  magnetic  de- 
clination should  also  be  correctly  shown  or  stated. 

2.  The  lengths  of  all  boundaries,  offsets,  and  tie  lines. 

3.  The  designated  name  or  number  of  the  tract,  block,  or 
lot;  if  the  land  is  part  of  a  subdivision  or  additon  to  a  town,  this 
fact  should  be  stated  and  the  official  record  of  such  subdivision  or 
addition  clearly  referred  to, 

4.  In  cities  the  names  of  streets;  also  bodies  of  water 
bounding  sane,  and  names  of  contiguous  owners. 

5.  The  angles  of  lines  of  adjacent  lands  v.rith  names  of  -ovmers, 
S.  A  plain  title,  a  scale,  and  a  meridian  arrow;  also  the 

date  of  the  survey  and  the  signature  of  the  surveyor  with  his  official 

title,  if  any. 

the 
7.  If  required,~recording  of  the  survey  with  all  parts 

complete —  notes,  map, etc,,  in  the  office  of  a  county  recorder,  with  a 
municipal,  state,  or  government  official  as  required. 

There  is  nothing  wrong  in  a  surveyor1 s  use  of  information 
of  such  character  in  the  further  prosecution  of  the  work  of  his  pro- 
fession, but  he  has  no  rights  of  monopoly  of  such  information. 


Surveying-IB  Assignment  39  Page  7. 

He  has,  when  vfork  is  done  as  above  detailed,  done  only  his 

duty;  if  he  has  done  this  conscientiously  and  correctly  his  rewards 
are  large  and  sure. 


Problem  to  Accompany  Assignment  39: 

As  a  problem  to  accompany  this  assignment  set  up  the  notes 
of  an  ideal  land  survey  giving  the  data,  sketch,  and  explanatory  notes 
in  acceptable  form.  Follow  the  specifications  given  in  the  assignment 
from  1  to  6  inclusive.  This  means  a  small  map  on  a  sheet  8  i  "  x  11". 
The  map  should  be  carefully  drawn  in  pencil  first  and  finally  inked. 
Do  careful  lettering  using  taste  in  all  the  work. 

Submit  this  as  evidence  of  your  having  profited  by  this  course 
in  Place  Surveying, 


•    - 


UNIVERSITY  OF  CALIFORNIA  EXTENSION  DIVISION 
Correspondence  Courses 

Surveying-IB      Elements  of  Surveying        Mr.  Swafford 

Assignment  40 

Rights ,  Duties,  and  Judicial  Functions  of  Surveyors . 
Foreword,  In  this,  the  concluding  assignment  of  this 
course  in  the  Elements  of  Surveying,  it  has  been  deemed  best 
to  further  call  your  attention  to  the  fact  that  while  as  a 
surveyor  you  have  certain  rights  due  to  your  quast -official 

position  and  irhile  certain  important  and  specific  duties 

*wt  tLAsV-C&''6~{£, 
must  compel  you  in  an  wwiefiireble  course,  you  are  also  hedged 

about  by  other  things  that  limit  the  scope  of  your  authority 
and  especially  your  judicial  functions. 
(277)     There  is  a  tendency  with  those  whose  education  and 

experience  has  been  along  mathematical  and  scientific  lines 
to  become  irnbued  with  a  high  regard  for  their  own  judgments 
and  conclusions.  A  training  along  such  lines,  however, 
should  render  you  modest  and  cautious;  it  should  make  plain 
the  fallibility  of  all  human  agencies;  it  should  teach  the 
exercise  of  deference  to  the  opinions  of  others  and  of  patience 
and  forbearance.   Instead  of  reaching  conclusions  hurriedly 
and  pronouncing  Judgments  boldly  a  scientifically  trained 
mind  should  take  note  of  all  phases,  evidences,  or  testimonies, 
balance  them  carefully,  and  draw  deductions  only  after  full 
deliberation. 

Again  a  hasty  or  faulty  conclusion  is  sure  to  carry  you 


Surveying- 13   Elements  of  Surveying.  Assignment  40,  page  2. 

into  error  that  must  later  be  rectified  by  much  labor  and 
sacrifice.   The  consequences  of  false  conclusions  are  often 
far-reaching  and  attended  with  confusion  and  loss  to  all 
concerned.  They  often  nrovoke  disagreement  and  expensive 
litigation. 

(278)     In  Assignment  20,  Art.  153  the  subject  of  the  location 
of  lost  and  obliterated  corners  of  the  rjublic  land  surveys 
•was  briefly  treated;  the  surveyor  who  assumes  to  attempt 
such  work  should  enter  upon  it  only  after  fully  understanding 
the  method  in  each  case  and  by  following  explicitly  and 
carefully  the  full  instructions  afforded  by  the  General 
Land  Office.  In  the  execution  of  your  duties  in  such  matters 
you  must  recognize  that  \-;hat  was  done  and  what  was  intended 
to  be  done  when  the  original  survey  was  made  may  be  at 
variance;  and  that  it  was  what  was  done ,  not  what  was  intended^ 
that  established  the  corners  and  their  connecting  lines  that 
stand  as  the  tangible  record;  and  that  this  record  must  not 
be  changed  for  any  reason,  whatever  the  findings  in  any  case. 
Vlfhen  you  have  to  the  best  of  your  ability  executed  the  com- 
mission intrusted  to  you,  your  own  status  has  not  been  ad- 
vanced  beyond  that  of  an  expert  and  you  should  neither  regard 
yourself  nor  permit  others  to  believe  that  you  have  any 
judicial  prerogative  whatever.  You  may  counsel  or  advise; 
you  nay  use  the  weight  of  your  knowledge  and  skill,  or  the 


Surveying-IB.   Elements  of  Surveying.  Assignment  40,  page  3. 

confidence  reposed  in  your  ability  arising  from  long  experi- 
ence and  conscientious  service  to  advise  or  concilliate,  but 
you  must  not  act  the  judge. 

(279)  Thus  it  v.ill  be  seen  that  the  relation  of  the  surveyor 
to  his  client  is  a  delicate  one;  that  he  owes  it  to  himself 
to  be  truthful,  nainstaking,  honest;  he  must  apply  the  know- 
ledge and  the  arts  of  his  craft  to  the  discovery  of  the  truth 
and  he  is  then  and  only  then  justified  in  urging  his  con- 
clusions and  findings  for  acceptance  by  those  he  would  serve. 

The  fallibility  of  man  and  the  imperfections  in  the  sys- 
tems of  surveys,  even  when  the  greatest  precautions  have  been 
taken  to  establish  and  monument  important  surveys,  have  called 
for  the  intervention  of  the  courts  in  myriads  of  cases  and 
have  called  for  some  notable  decisions  which  have  a  historic 
as  '.veil  as  a  iudicial  bearing. 

The  surveyor  is  not  called  upon  to  know  the  law  as  ex- 
pressed in  these  decisions,  but  it  is  expedient  that  he  should 
know  hov  these  laws  may  affect  the  rights  of  his  client,  for  he 
may  be  asked  to  advise  or  arbitrate,  and  then  a  knowledge  of 
legal  decisions  and  rulings  "rould  assist  his  judgment. 

(280)  "In  making  a  resurvey  where  there  is  considerable  un- 
certainty, as  in  the  case  of  disputed  boundaries,  the  surveyor 
has  no  official  power  to  decide  any  disputed  point.  He  can  only 
act  as  an  expert,  and  give  an  opinion  as  to  what  is  the  most 


Surveying- IB.  Elements  of  Surveying.   Assignment  40,  page  4, 

probable  solution  of  the  difficulties  in  question.  If  the 
interested  parties  do  not  agree  to  accept  his  decision,  the 
question  must  be  settled  by  the  courts."   (Quoted  from 
Gillispie's  Surveying.) 

A  code  of  rules  for  the  guidance  of  surveyors  is  found 
in  the  above  work  on  pages  346-351.   The  student  of  this  course 
is  advised  to  make  himself  familiar  with  them. 

Another  compilation  of  valuable  instructions  is  to  be 
found  in  a  paper  prepared  for  the  Michigan  Society  of  Sur- 
veyors and  Engineers  by  Justice  Cooley  of  the  Michigan  Supreme 
Court.  A  roprint  of  this  paper  is  found  in  Raymond,  and  also 
in  Johnson,  to  which  the  student  is  referred.  This  and  the 
foragoine;  "rules"  have  become  "classics"  of  the  subject, 
"The  Judicial  Functions  of  the  Surveyor."  These  then  taken 
together  with  the  court  decisions  above  referred  to  consti- 
tute the  "code"  of  the  surveyor  and  should  be  relied  upon 
for  guidance  in  his  avork. 

(281)     A  few  quotations  follow,  taken  from  several  sources, 
and  designed  to  show  the  scope  and  limitations  besetting 
the  surveyor; 

"No  statute  can  confer  upon  a  county  surveyor  the  power 
to  'establish'  corners,  and  thereby  bind  the  parties  con- 
cerned. Nor  is  this  a  question  merely  of  conflict  between 
state  and  federal  lavr,   it  is  a  question  of  property  right." 

"In  any  case  of  disputed  lines,  unless  the  parties  con- 


Surveying-IB.  Elements  of  Surveying.  Assignment  40,  pags  5. 

cerned  settle  the  controversy  by  agreement,  the  determination 
of  it  is  necessarily  a  judicial  act,  and  it  must  proceed  upon 
evidence,  and  give  full  opportunity  for  a  hearing," 

"Nothing  in  -what  has  been  said  can  require  a  surveyor  to 
conceal  his  ov;n  judgment,  or  to  report  the  facts  one  way  when 
he  believes  them  to  be  another.  He  has  no  right  to  mislead, 
and  he  may  rightfully  express  his  opinion  that  an  original 
monument  was  at  one  place,  ivhen  at  the  some  time  he  is  sat- 
isfied that  acquiescence  has  fixed  the  rights  of  parties  as 
if  it  were  at  another.  But  he  would  do  mischief  if  he  were 
to  attempt  to  "establish"  monuments  which  he  knew  would  tend 
to  disturb  settled  rights;  the  farthest  he  has  a  right  to  go, 
as  an  officer  of  the  law,  is  to  express  his  opinion  where 
the  monument  should  be,  at  the  same  time  that  he  imparts  the 
information  to  those  who  employ  him,  and  who  might  otherwise 
be  misled,  that  the  same  authority  that  makes  him  an  officer 
and  entrusts  him  to  make  surveys,  also  allows  parties  to  settle 
their  ovm  boundary  lines,  and  considers  acquiescence  in  a 
particular  line  or  monument,  for  any  considerable  period,  as 
strong,  if  not  conclusive,  evidence  of  such  settlement. 
(282)     Reasonable  persons  are  inclined  to  give  weight  to  the 
findings  of  an  expert,  as  the  surveyor  is  supposed  to  be, 
and  if  he  has  also  the  authority  of  a  public  office  to  support 
hife  findings,  they  are  likely  to  be  convincing.  But  he  must 


Surveying-IB.  Elements  of  Surveying.  Assignment  40,  page  6. 

not  assume  that  his  decisions  aro  final  as  the  courts, 
though  competent  testimony  and  other  convincing  evidence  may 
modify  or  reverse  the  conclusions  of  the  surveyor. 

r'fhen,  in  case  of  disputed  boundary  the  surveyor  is  called 
uoon  to  render  the  service  of  locating  monuments  or  running 
lines,  after  a  complete  finding  as  to  the  true  facts,  they 
should  be  submitted  to  the  parties  concerned  with  no  attempt 
to  urge  upon  either  what  would  not  be  exacted  of  both.  In 
other  words  the  disputants  should  be  led  to  see  the  facts  as 
revealed  in  the  survey  and  to  regard  these  as  of  import  to 
both.   To  secure  a  final  settlement  it  is  necessary  that  they 
.ipree  to  abide  by  the  survey,  and  of  course  to  make  this  bind- 
ing the  agreement  should  be  reduced  to  writing  and  properly 
drawn  and  recorded.   No  parole  agreement  can  secure  the  title 
as  to  Property  rights. 

(282)     In  conclusion  let  us  urge  that  you  exercise  both  tact 
and  modesty.   You  must  not  assume  an  arbitrary  attitude  nor 
permit  yourself  to  mislead  employing  parties  to  believe  that 
you  ire  possessed  of  authority  when  you  have  none,  or  that 
your  findings  t>ro  final  and  inflexible.   The  courts  are  the 
only  "last  resort"  of  parties  who  disagree  and  disputants 
who  cannot  settle  their  differences  otherwise  must  do  so  in 
the  courts. 


Surveying-IB.    Elements  of  3u/in§'  Assignment  40,  page  7. 


Questions!  Problems 


1.  Show  by  diagram,  fully  d(ilecit  how  to  proceed  in  laying 
out  the  south  half  of  t  N«'^»  quarter  of  section  15  in 
T6N,  R4B,  assuming  tha;ne  ^^  township  corners  on  the 
south  are  located. 
2.  How  are  the  four  quari  section  corners  of  section  6 

in  any  township  locad? 

3.  A  rectangular  city  b-k  was  subdivided  into  12  lots  of 
uniform  size  50'xl,' »  making  the  block  dimensions 
300'  x  350',  A  refvey  to  locate  the  corners  of  lot  #3 
revealed  that  thelock  dimensions  were  actually  304.8ft. 
x  247-5  feet,  v/ha-should  the  dimensions  of  lot  #3  be, 
and  by  what  mea^ements  should  the  corners  thereof  be 
determined? 


1 

2 

3 

4r 

5 

6 

iwlnj 

10 

9 

8 

7 

4.   For  each  of  the  above  cases  (given  in  problems  1,  2,  3) 

state  britfly  the  functions  of  the  surveyor,  and  indicate 
how  those  functions  are  limited  by  law  and  practice. 


-:    ;    ;    : 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 

This  book  is  DUE  on  the  last  date  stamped  below. 
LN&lNLEKiNG   LlbhiM(.. 


MAR  1 6  19! 


LD  21-100m-9,'48iB399sl6)476 


YE  03760 


793909 


TAri 


Engineering 
Library 

UNIVERSITY  OF  CALIFORNIA  LIBRARY 


